What I've experienced working well is to consider platform/infra as just another dev team. They should experience the same good practices (staging changes, tests, documentation, clean code) and duties (level 2 on calls, regular postmortems from ops, etc).
Ops/prod/support eng are generally more business related and less technical than infra/platform. They make sure the processes run as they should, or operate with agreed procedures when something is raised. Some issues may be lightly technical ("theres an alert on free disk space of server X", "provider Y changed their SFTP keys without notice", etc) and some business related ("provider Z is late to push updates", "it's a holiday on country of provider A", "service of team B raises an exception when situation C occurs"). They are often level 1, in between the actual dev teams (escalating issues to them, or asking for better stability, logs, resiliency, etc) and the platform/infra team.
Being faced with production issues is a burden for focus, etc. I wouldn't want my platform team to be on level 1 handling these stuff or nothing get done.
Still, I wouldn't want them to be completely free from it or they would loose track with reality, just as any other dev team.
To summarize, I would say:
- A fleet of business dev team
- A fleet of platform / infra team
- A support/ops/prod team handling level 1 through procedures written by dev/platform teams, and raising to infra or business dev for level 2. Regular feedback sessions with each other team to have them stay on touch with real life. Some light coding / improvements tasks paired with infra or dev to get them a better understanding of the underlying layers.
From the description you provided, that's what I would call a "platform engineer". Though the titles are sensitive for some people, and there's a lot of discrepancies between companies, so i usually let people from platform choose the title they prefer, between SRE / DevOps / platform eng / cloud eng / infra eng.