how does Slack generate subdomain SSLs for new/all team subdomains? Can we use letsencrypt?

Automation using Letsencrypt?

Wild card certs for all sub-domains of a domain via Letsencrypt is now possible.

Not sure, how Slack does it, but Caddy webserver does this all behind the scenes without you having to do anything. First request comes in, and it issues a SSL cert for that domain before responding to that request and keeps it renewed.

Caddy seems to be paid? Is that possible with Apache or Letsencrypt? Google is not giving any good answers for this.

Yes, automation is possible with Apache or Nginx as well. Caddy is open sourced, you will have to compile. If you just wanna use compiled binaries, you gotta pay.