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I found that secp384r1 is supported in almost all web browsers and it is considered secure.

My question is:

Is it okay if i use only secp384r1 and up named groups? Are there any disadvantages considering that the server is only accessible with TLSv1.2 and up so browser support issues are almost non existent?

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It seems to me that according to ssllabs.com, supporting only TLS 1.2 (or TLS 1.2 and TLS 1.3), only ECDHE with secp384r1 (no DHE, no RSA key exchange without PFS), should get you support by all the TLS clients you would care about. If in doubt, try ssltest with your server configured the way you want. You can/should try a dev server before changing config on prod.

secp384r1 is not a very good curve - it is too slow for its security level - but it should be fine. It is less used than secp256r1 so maybe the implementations are less reviewed or less optimized, but you probably don't care.

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