What’s the industry standard on how to auto push new features to production?

I work on a small dev team (like 10 of us) – and currently we are sort of manually picking which files to move from our staging server to production. We use GitHub to house and build new features, but then also sort of move files over manually to staging to test (none of the environments are connected to repos. So we don't really have any automation built in. I know we can use GitHub actions to create a pipeline but our issue is that some PRs need to stay in staging for more testing/fixes, but some can be pushed into production.

Is there a way to pick and choose which PRs go into production from staging (or something similar).