1) "safe spaces" for emotions is inherently at odds with corporate culture, point blank. They exist to use you. They pay you, you provide them a service and/or your time as written in the contract. It is in your best interest to not be the nail that sticks out from the wood if you wish to keep the money coming because ultimately the power exchange lies heavily with them.
2) I don't do support groups, though this is more of a personal decision. Keeping vulnerable facets of my life completely air-gapped from cash flow and from other untrusted and un-vetted individuals has never failed me.
Now - water cooler-ish 1:1's a la "hey, you hanging in there?" can be done with tact and sincerity by select individuals if there's a previous rapport. But there is an art to sniffing out whether it's meant with a sincere no-bullshit-humanity-centric angle, versus "can we optimize this individual's output" angle. It's demeaning to think one can be the other.