Follow up:
Spoke with CSR customer service and they confirmed that I would still get full CSR benefits even on PayPal, as they code transactions based on the end merchant. United would code as “travel” and any travel related benefits would kick in, so long as a “portion” of trip is paid using CSR card.

I then called United Explorer Chase customer service. She confirmed that using PayPal on United app with a United branded credit card still gets pushed through the system to UA as a United branded credit card transaction, all travel and baggage benefits are recognized. I asked about a partial payment for an airfare and she said that would be a UA operational decision.

So finally I connected to UA customer service. She confirmed to me that PayPal wasn’t an issue so long as I used my United card to pay for the fare. It should still come through in their system as a fare paid for with the United branded card. She wasn’t sure about the partial fare issue. She read thru the T&Cs and in her view I should still get the 1st free bag.

I’m currently United Silver, but doubt I will retain my status for next year. This is for an itinerary in 2024.

I ended paying via PayPal, but doing a few more cents of the reservation on the United Explorer card. It’s currently showing my reservation as getting a free checked bag, but unclear if that’s due to the United credit card or my current status level (TBD).

If anything, this is a nice hack to juice more points on CSR which gives you 3x points for every $ spent (vs. 1 mile per $ spent on the United Explorer card).