(I just checked and couldn't get a definitive answer but since it's been 5 years [1] since there was any update on a ticket requesting the ability to offer invoices in PDF form of your monthly receivables, my gut instinct says the answer is still, "no")
Payers are obligated to issue tax-related forms in certain circumstances. But the receivers don't even need those to file their own tax paperwork.
Your payment processors (PayPal and Stripe) absolutely do provide tax forms. Its your responsibility to make appropriate use of them. But Liberapay itself doesn't have forms it needs to provide (and by god you don't want to provide tax forms or tax advice you aren't required by law to give)
Nowhere in this statement does it say "gift rules only apply to friends and family"
If you reach the point where a substantial portion of your income is Patreon or whatever (and thus, you wouldn't be otherwise performing the entertainment service), I'm sure the IRS would view it differently.
"a recipient generally can exclude from gross income for federal income tax purposes a donation from a nongovernment donor as a gift if the donation is motivated by detached and disinterested generosity and is not in anticipation of an economic benefit or in return for services."
ref https://www.irs.gov/pub/irs-wd/03-0025.pdf and Commissioner v. Duberstein, 363 U.S. 278 (1960)
perhaps, my categorization of "more than likely" could be incorrect. But given how relatively small[0] most accounts make on Liberapay, that is what I imagine most in the US would be calling it.