Current t allows texting and calls outside of session. Texting was very weird at first, and I still try not to abuse it much (though sometimes I feel like I text too much). One of the goals of therapy for me is to reach out and ask for support when I need it (rather than end up in the hospital or seriously self-harming). It's taken me a few months, but I'm now at a point where I can text "just to check" and that usually helps me feel less alone when struggling. She keeps insisting it's not bothersome or annoying, so I take that at face value. Occasionally, i'll text something specific about whatever I'm struggling with, and we either have a brief text exchange, or she calls.
She's also open to additional sessions as needed (and she has availability).
I'm not sure she does email, never asked.

Previous t's have had varying policies around outside contact. One was cool reading private blog entries, most would return calls during office hours. A few had clinic crisis lines accessible after hours. Current t has the most lenient outside contact yet. I'm not sure how she does it because she specializes in trauma, which means most her clients have a high likelihood of needing additional support... she's been doing it for a long time though, so she must be taking her own needs into account.