I'm in the same position. I've been using Xcode 11 on macOS 10.15 for the last few days to play around with some of the new Swift stuff. I've made several very small "Hello World" style applications.
Xcode 11's build system was quite buggy with numerous failures being shown even though the build was successful. But at least it was "working"... Up until this morning.
Since waking up this morning and trying to use Xcode, I'm stuck with "Indexing..." as well. One small project builds, but another doesn't. It worked fine a few hours ago!
I have "SourceKitService" and two "swift" processes running in Activity Monitor each around 90% CPU utilization. The Xcode activity bar says "Indexing..." but the process bar is not moving.
Like you, I've tried deleting every Xcode folder I can think of but to no avail. Rebooting didn't help either. There must be some other hidden folders where Xcode is caching data...
At the moment, Xcode 11 just became unusable for me and it's not obvious how to "Reset" it to whatever condition it was in last night when it was working...
Created a new project to figure out if it’s a problem with Xcode or with my project and the newly created project would build without problems.
So, then I went throgh the code changes of the project where I came across the same “Indexing...” problem. After resolving syntax errors that had not been automatically detected, Xcode was back to normal.