TIL (in v3.2) the browser will send out the reduced ‘(Linux; Android 10; K)’ UA string, while the webview will (as your link shows) ‘(Linux; Android 10; Pixel 4a Build/QD4A.200805.003)’. Cromite doesn’t enable kWebViewReduceUAAndroidVersionDeviceModel yet (there’s some adjacent keys too).
Android 16 will bring User-Agent Reduction to the Webview on stock too. The jucier infobits will move to Client Hints and behind a getHighEntropyValues() call - wonder what the login portal vendor you struggled with will do about that.
I’d probably abandon the hardcoded patch, enforce ua-reduction on the webview and report the Android major truthfully.