I have been contending with this AADAP Failure as a new user since February and think I have a fix.

Step 1:
Login to https://entra.microsoft.com/

Step 2: Expand "Applications" and Select Enterprise applications

Step 3: Hopefully you should see "2 applications found"
             One should say Sage Business Center
             The other should say your PC-NAME the proxy should be installed into
              Click the blue link of that PC-Name, something like PC-NAME_Sage100ContractorTime_UniqueID

Step 4: Inner Left Side Menu > Manage > Select Application Proxy

Step 5: Look for this text at the bottom of the page

           We recommend at least two active connectors in selected group
           'PCNAME_Sage100ContractorTime_UniqueID_CG'.

Step 6: Click the Link that says, Click here to download a connector or manage your connector groups

Step 7: Hopefully you're on Private Network connectors page that shows the PC you trying to configure
             Here is a direct link to help:

            Private Network connectors - Microsoft Entra admin center

Step 8: At the top menu click Enable Private Network connectors

Step 9: Try to reinstall the proxy 

Hopefully you receive "Proxy for mobile apps is installed " and the diagnostic tools appear in the database admin tool!

I'm not saying this is the end all fix to this problem, but it fixed my issues!

Good Luck

I have been contending with this AADAP Failure as a new user since February and think I have a fix.

Step 1:
Login to https://entra.microsoft.com/

Step 2: Expand "Applications" and Select Enterprise applications

Step 3: Hopefully you should see "2 applications found"
             One should say Sage Business Center
             The other should say your PC-NAME the proxy should be installed into
              Click the blue link of that PC-Name, something like PC-NAME_Sage100ContractorTime_UniqueID

Step 4: Inner Left Side Menu > Manage > Select Application Proxy

Step 5: Look for this text at the bottom of the page

           We recommend at least two active connectors in selected group
           'PCNAME_Sage100ContractorTime_UniqueID_CG'.

Step 6: Click the Link that says, Click here to download a connector or manage your connector groups

Step 7: Hopefully you're on Private Network connectors page that shows the PC you trying to configure
             Here is a direct link to help:

            Private Network connectors - Microsoft Entra admin center

Step 8: At the top menu click Enable Private Network connectors

Step 9: Try to reinstall the proxy 

Hopefully you receive "Proxy for mobile apps is installed " and the diagnostic tools appear in the database admin tool!

I'm not saying this is the end all fix to this problem, but it fixed my issues!

Good Luck

Was this issue resolved with the 26.1 release last week?

Unfortunately, No
The 26.1.154.0 Update gave me the same issue.  "Failed to install proxy" AADAP Failure

Been with tech support for 2 days now waiting to see a resolve.
I decided to dig in and got it resolved on my own.

There are many pieces involved getting this setup and only takes 1 to break.
My issue may not be yours, but worth the try.

Thanks for the info, Troy!

I got mine fixed in mid-April.  I worked with a support lady and first she remoted in and said that I didn't have IIS installed on my computer.  Still got the error message.  The support lady from Sage worked and worked and finally had me change my password for the Microsoft  online admin.  And then it worked.  She had me change some special charaters and not end it in a number.  Simple Time works great now.  Our guys really like it.  Good Luck!