Been working with Ezra from billing on this issue.
Trying to buy some number of yearly credits (I've tried $120.00 for the mid-tier plan with US tax, I've also tried $75.00 for the lowest-tier plan) via PayPal. When I click the PayPal button, the PayPal browser window appears very briefly and then disappears.
Your bugtracker suggested an issue opened by "pixel" in 2023 that has a summary that sounds really similar, but I haven't seen the comments so I don't know if it's related or not.
I've tried both my main browser (Firefox) and Microsoft Edge and the results are the same. I have no extensions loaded with Edge, and I have uBlock Origin turned off for kagi.com for firefox.
Attaching videos of each browser, taken with Nvidia's built-in "ShadowPlay" recording.
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Ideally you would allow recurring billing through PayPal.
Without that, though, I'm happy enough that you allow annually buying "credits" (KagiBucks!) and then applying them to my account.
The PayPal integration just doesn't seem to be working, though.