The main thing I want is to remotely generate new bitcoin addresses. How do I do this?
you can use BTCPay API and Connecting Electrum Wallet to BTCPay Server.
Here are some topics that can help you get work done:
Using the BTCPay API for Custom Integration --->
https://docs.btcpayserver.org/CustomIntegration/Connecting Electrum Wallet to BTCPay Server --->
https://docs.btcpayserver.org/ElectrumWallet/Finally, you need to keep the address on a computer that did not connect to the Internet (Air gap,) or link a hardware wallet with it.