I have been with my current therapist for 8 years so I have had a chance to go in and out of a lot of "phases" with my therapist.
This would be one of those "phases". Still today I can't wait until I get to therapy but I think that is due to the huge mind dump I can do and can be guided that week. And I can also tell when I have to skip a week. But I don't think about him between sessions like I used to and I don't totally obess. I never really did obess but I did do everything you stated here. I still think about him (non-sexual) at night to help me sleep and he states that is normal as it makes me feel safe.
But early in, maybe a year or so in for a few years, I felt as you described. Would say completely normal, fully expected, and shows of a good relationship building in my opinion.