My experience has been that I and my friends feel close even if we don't talk very often. One friend and I have been friends for 40 + years. The other for 30 years. I can talk to both of them about anything any time. We do not talk every week. We just know the other one is there.
I'm 73 and have friends come and go over the years. As life changes, friendships change. I am feeling a bit bereft because one of those friends has Parkinsons and dementia. Another friend recently died. I have made a couple of younger friends but we aren't as close as my long term friends. In part because we lack having a way of life in common.
I'm developing a new, same age friendship after asking for advice. She was a neighbor when our girls were young. Being neighbors and having girls who were friends were the only things in common back then. We've just reconnected and found we have more in common at this age.
I wonder what is your question? From your previous posts, I wonder if you don't feel connected and are thinking weekly contact would help with feeling connection. I suggest it won't. We feel connection because we have things in common and because we share love.
It sounds like you feel you're missing something. I wonder if it would help if you organized your days. Plan times to spend with friends. Your post about working from home and you having difficulty with procrastination seems to me to be very unsatisfactory. I procrastinate and would never be able to work from home. I was better organized about household tasks when I was going to work elsewhere. Now that I'm retired my house is a mess.
Perhaps if you worked out a daily schedule and focused on mostly keeping to it, as if you were working in an office would help, not only with feeling more successful at home but also in your friendships. You can be flexible while not letting anything to change what you need to do for work.
Perhaps have a separate phone for work and only answering that phone at times you've scheduled other things or get caller ID and when you're occupied only answer work related calls. Decide what hours will be work hours and plan how to help your kids not to interrupt you. It sounds like you are easily distracted. Figure out ways to keep yourself focused.
If you want to connect with friends every week, plan how you can do that. With one friend who wanted more physical connection she came to my house for pizza every week. With the other close friend we don't plan for a regular meeting but seem to still get together a couple of times a month. Same with the new friend. I've talked with friends about how I feel and they feel. For me, sharing feelings is what keeps us close.