No popup window for downloads, saves in Chrome; can't upload unless drag and drop?

As the User is relying to themselves - it is difficult to know to Whom the above is intended

As for Third Party Software not playing well with Monterey - it is the responsibility of the Software Maker to make their Software compatible with Monterey not the Other way around.

Developers have had Advice Access to Beta Versions before it was released to make sure their Software would or would not work in Monterey.

It is also good computer practices for the User ( you ) to verify that existing installed Third Party Software will work with Monterey.

1 - Restart in Safe Mode. This will perform a Disk Repair, clear cache files and only load Apple Software, extensions and fonts. The boot up will be slow and can take some time - Normal.

2 - Does the issue present in this mode ?

3 - Sometimes a Safe Boot followed by a Normal Boot will just put things right.

4 - If not - there could be something in the main User Account playing up. To further isolate this - Set up users, guests, and groups on Mac. Then log out of the Main User account and log into the dummy account and test again if the issue persists.

5 - If the issue is present in the dummy account - then, this appears to be a System Wide issue on the computer.

6 - If after performing each of the above steps in the order that have been presents and still have issues - please advise for possible further assistance.

Please run Etrecheck and post its full report here. Use the "additional text" button and paste the report into the text box.

Further, as per user profile running Monterey version 12.3 which is no longer up to date.

The current version is 12.4 , as of this writing, released in May 16.

Suggest doing a Time Machine Backup before attempting

If you’re having issues with Chrome, contact Google support.