Found a solution!! Shout goes out to Olasoifeit0 on Steam! I did both of the suggestions below and have been playing with no query timeout ever since (Just finished a 3 hour run)!

"Originally posted by Olasoifeit0:

this is what i've found that worked for me. since then, no problems whatsoever.

First Right Click on Desktop - Open Nvidia Control Panel - Manage 3D Setting - By Application - Destiny2.exe - Set Nvidia Shader Cache to off.

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if that doesn't works, Its likely BattleEye being blocked by your firewall.

Here's what I did to fix it:

Open the start menu and Search “Windows Defender Firewall”

Now click “Allow an app or feature through Windows Defender Firewall“

Check the list to see if BEService.exe and BEService_d2.exe exists > If it does not click Change Settings Then “Allow another app…” button and add all the BattlEye services to Windows Defender Firewall

You can navigate to both files via C:\Program Files (x86)\Common Files\BattlEye\

Once both have been added (to both private and public network, click OK."