have also experienced this same problem.
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also seeing the same issue: no way to download and install the 10.15.6 beta update.i went to the extent of hitting the "Details" link under the "Software Update" icon in the left tab of the System Preferences->Software Update panel, and it offered "This Mac is enrolled in the Apple Developer Seed Program. Do you want to restore default update settings? Any previous updates will not be removed and this Mac will no longer receive beta updates"i tried hitting the "Restore Defaults" button, then re-applying the macOSDeveloperBetaAccessUtility.pkg from the beta downloads site, but the effect is the same: Software Update does not offer a way to update.