What would your ideal therapeutic relationship look like?

I would say my current therapy relationship is probably as close to my ideal as it's possible to get.

The upsides:
Current TR is alternating weeks online with f2f. Online lasts an hour, f2f lasts 90 minutes; sessions do run over if we are in the middle of processing something, she never just cuts it short.
In-between contact is allowed by email or text. I use it mainly for communicating things I have problems verbalising, and then we'll use it as a basis for discussion in session. I never expect a reply from T, although she does sometimes send a brief reply.
She allows a hug at the end of the session if I want it.
T has very few actual boundaries (at least none that I've bumped up against).
T shares personal information if she thinks it will be helpful. She doesn't give advice, but will make suggestions if she thinks it will be useful but there is never any compulsion to take it.
T understands the complexities of being a Carer because she is one. She also understands the challenges of living with a specific neurological condition, one that ironically, I share with her partner, so she understands that from the inside out too.

The downsides:
T sometimes over-shares a little too much.
The carer side of her life occasionally gets in the way of sessions and we might need to reschedule.
She lives too far away to do f2f every week, so every other week is a compromise.

Despite the challenges of her dual-life, I would not swap my T for anything.

I've been to a few therapists over the years. Some were okay and at least one was truly harmful. My current one is by far the best.

I need a therapist...

-who is intelligent, grounded and has done their own work

-who understands trauma and attachment and isn't going to get entangled in an enactment with me.

-who has safe boundaries but also isn't afraid to share some of themselves too. My T lets me into his life without making it about him, or over-divulging personal stuff. But he answers any questions I have and even sends me photos of beaches and mountains when he's on vacation.

- who isn't afraid to give a hug if a client wants one and would benefit from that.

-who shows love and care but also doesn't encourage over-dependence on therapy or the therapist. This one is huge and lately these forums have made me appreciate my T's insistence that I keep my own power and don't give it away to anyone, especially not to a therapist (who by nature of the relationship dynamic already holds a lot of power).

For me, it would be:
Options to meet more than once a week
Email within reason is allowed
Allowing some sort of touch, but not as a regular thing, but also not a deal breaker
I'm fine with 45 - 50 minutes, but I prefer longer vs shorter
No blank slate
In person is the norm, with an option for online as needed

I'm answering this through the lens of my relationship with P. There has always been a "chemistry" of sorts between us. If I were to have a new therapist where I didn't feel that chemistry, I might feel differently about some of these things. For example, my NP prescriber, who I also do sessions with about every 3 to 4 weeks, offered me a hug one time and I turned him down. I didn't feel comfortable enough with him for that and I might never want any sort of touch from him. I also have no desire to email him while I do have that desire with P.

As long as were getting detailed I have more to add

A relaxed bohemian vibe in office and person, ideally an office in an house not an office building. Eclectic and variability in psychological approach to the process. Willingness to talk politics as that is something that causes much anxiety. Communication by text and email to schedule appointments and such. No need of regular contact outside of office hours. Sessions being 50 minutes. Like to end sessions with lighthearted talk of art or literature. All my Ts had office buildings a house would be a nice change. Also within 10 minutes drive or less and ample parking.