Calendar with Correlating Data. Please Help!!!

As per my comment on your other post, I've had a good look at your code and make the following observations:

1. Your PersistenceController is a struct and you reference it a number of times in your Views e.g. PersistenceController().removeFromItem(item: items[0], context: managedObjContext), which means that your CoreData stack is being recreated each time (ie numerous copies) - with unpredictable results. The PersistenceController needs to be an ObservableObject class singleton, i.e. with let shared =PersistenceController(), and then refer to the shared instance.
2. the date that you set from the calendar picker is the time of picking, i.e. date and time, so your predicate, which also uses the current date and time, will probably never match. I assume that you're looking for an item (or items) that occur on a selected day (date only, not time). The predicate therefore needs to search for a timestamp that occurs within the start and end of a day (date).
3. It's not clear where, or if, you created the @StateObject for the @Environment(\.managedObjectContext) var managedObjContext, without which the @FetchedResults are unlikely to work (plus the problem of multiple CoreData stack instances).
4. When the above issues are resolved, there remains the problem of getting SwiftUI to re-execute the Fetch on a change of date i.e. a dynamic predicate with immediate effect.

I've created a working version of your code, but without the FetchRequest and Results in ContentView: I use a fetch function in PersistenceController to return Items with a timestamp that falls within the specified day (midnight to 11:59:59pm). When the selected date changes, the function gets called to return the item(s) for that date. That's the item (or item array) that then gets used in your existing code.

I'll post the full solution tomorrow morning (about 00:00 UTC Sunday 26 June ) after I've further tested it.

Regards, Michaela

Main Struct

@main
struct TestForWeagleWeagleApp: App {
    let persistence = PersistenceController.shared  // initiates the CoreData stack
    var body: some Scene {
        WindowGroup {
            ContentView()
        }
    }
}

Persistence

import Foundation
import CoreData

class PersistenceController : ObservableObject {
    static let shared = PersistenceController()
    let container: NSPersistentContainer
    init(inMemory: Bool = false) {
        container = NSPersistentContainer(name: "Test")
        if inMemory {
            container.persistentStoreDescriptions.first!.url = URL(fileURLWithPath: "/dev/null")
        }
        container.loadPersistentStores(completionHandler: { (storeDescription, error) in
            if let error = error as NSError? {
                fatalError("Unresolved error \(error), \(error.userInfo)")
            }
        })
        container.viewContext.automaticallyMergesChangesFromParent = true
    }

    func addItem(date: Date){
        let context = container.viewContext
        let item = Item(context: context)
        item.timestamp = date
        item.word = nil
        contextSave()
    }

    func addToItem(item: Item) {
        item.word = "Test"
        contextSave()
    }

    func removeFromItem(item: Item){
        item.word = nil
        contextSave()
    }

    func contextSave() {
        let context = container.viewContext
        if context.hasChanges {
            do {
                try context.save()
                self.objectWillChange.send()
            } catch {
                print("**** ERROR: Unable to save context \(error)")
            }
        }
    }

    func getItemsFor(_ date: Date) -> [Item] {
        let context = container.viewContext
        var request = NSFetchRequest<Item>()
        request = Item.fetchRequest()
        //request.fetchLimit = 1
        request.entity = NSEntityDescription.entity(forEntityName: "Item", in: context)
        request.predicate = NSPredicate(format: "timestamp >= %@ and timestamp <= %@", Calendar.current.startOfDay(for: date) as CVarArg, Calendar.current.startOfDay(for: date).addingTimeInterval(86399.0) as CVarArg)
        do {
            let items = try context.fetch(request)
            if items.count == 0 { return []}      
            return items.sorted(by: {$0.timestamp! > $1.timestamp!})
        } catch {
            print("**** ERROR: items fetch failed \(error)")
            return []
        }
    }
}

ContentView

import SwiftUI
struct ContentView: View {
    @ObservedObject var persistence = PersistenceController.shared
    @State private var items = PersistenceController.shared.getItemsFor(Date())
    @State private var date = Date.now
    var body: some View {
        NavigationView{
                VStack {
                    DatePicker("Calendar", selection: $date, in: Date.now...,displayedComponents: [.date])
                    .datePickerStyle(.graphical)
                    .onAppear(perform: {
                        if items.isEmpty {
                            persistence.addItem(date: date)
                            items = persistence.getItemsFor(date)
                        }
                    })

                if !(items.isEmpty) {
                    PlannedMealsView(item: items.last!)
                    Spacer()
                }
            }     
            .navigationBarTitle("My Planner")
        }
        .onChange(of: date){ newDate in
            items = persistence.getItemsFor(newDate)
            if items.isEmpty {
                persistence.addItem(date: newDate)
                items = persistence.getItemsFor(newDate)
            }
        }
    }
    func getTitle(date: Date)->String{
        let formatter = DateFormatter()
        formatter.dateStyle = .medium
        return formatter.string(from: date)
    }
}

PerformanceMealsView

import SwiftUI
struct PlannedMealsView: View {
    @ObservedObject var persistence = PersistenceController.shared
    var item: Item
    @State private var forceRefresh : Bool = false
    var body: some View {
        VStack{
            Text(item.timestamp!, style: .date)
                .font(.title2)
                .bold()
            Section("Word"){
                if(item.word != nil){
                    HStack{
                        Spacer()
                        Text(item.word!)
                        Spacer()
                        Button(action: {
                            persistence.removeFromItem(item: item)
                        }){
                            Image(systemName: "minus.circle").bold()
                        }
                        Spacer()
                    }
                } else {
                    Button(action: {
                        persistence.addToItem(item: item)
                        forceRefresh.toggle()
                    }){
                        Image(systemName: "plus.circle").bold()
                            .padding(.vertical, 10)
                            .padding(.horizontal, 20)
                    }
                }
            }
            Spacer()
        }
    }
}

This works on my system, except that (probably unwisely) I used my development environment, which uses beta Xcode and beta iOS. I couldn't backwards convert the Xcode project (new format) to test on my production equipment without redoing everything.

I hope this works for you too!!! Regards, Michaela