These third-party services will run/deploy BTCPayServer on your behalf. You won't need to buy a hosting server or run bitcoin full node but you will clearly have some limitations as you can read on that article.
Bitpay, coinpayments are some. But I hate them as much as I do paypal. And recent times I heard coinpayments are restricting some countries too. Bitpay already have some countries block.
By the way OP, if I am not wrong then you can try Blockchain.com API if you want. Again there are limitations.
Also check this:
https://www.a2hosting.com/blog/accept-bitcoin-payments/The third one seems interesting.
3. Accept Payments Manually
One of Bitcoin’s main selling points is that you don’t need to rely on third-party services to use them. If you want to, you can accept Bitcoin payments on your website without having to go through another platform.
The process is relatively simple – just
generate a Bitcoin address for each sale you make on your site, and provide instructions for how much money people should send. You’ll receive the coins in your wallet, and you can process the order as soon as the transaction is confirmed.
Of course, if you use this method, you’ll have to take care of invoicing and billing on your own. You’ll also need to arrange delivery for any items or services you sell, and provide payment addresses manually. This is potentially a lot of work, but it does cut out the middleman. That makes this method ideal for websites that only need to accept Bitcoin payments from time to time, or that see small sales volumes.