Is RSA in decline across the board? From what I gather from the internet (source), the recommended practice for 2019 and beyond is to avoid RSA and use ECDH and ECDSA.

Is this the general case?
RSA for key exchange is declining rapidly and is not recommended because it does not provide forward secrecy. Without forward secrecy, if someone breaks into the server and obtains the private key, they will be able to fully retroactively decrypt all recorded traffic encrypted under that key. ECDH does not have that problem because the private and public keys are generated on-the-fly, and discarded after use. This is possible because ECDH (and DH) key generation is light and easy on the CPU, whereas RSA is not. Generating a new RSA key pair for each key exchange would be absolutely prohibitive.

RSA for certificates, on the other hand, is still alive and well, and is still considered industry standard. There are some benefits that ECDSA has, though, such as smaller public key and signature sizes, which equates to reduced network usage, but verification with ECDSA is a little slower than with RSA.