Right now it's impossible to install LSP-json, here's what the details page shows:

The tooltip on "missing" reads:

Package info was unavailable last time crawler ran. Error downloading repository. HTTP error 429 downloading https://raw.githubusercontent.com/sublimelsp/repository/main/repository.json.

This affects many packages, here's what search by lsp- shows:

A few hours ago all LSP-* packages were missing, now some of them are back.

As a result, LSP-json is missing from the manifest (https://packagecontrol.io/channel_v3.json) and can't be installed with "Install package".

This is likely related to a recent GitHub rate limiting change reported here: https://github.com/orgs/community/discussions/157887.