PIP and Sheltered Housing

I live alone in a one bedroom flat and I've been offered a flat in sheltered housing from a different council to my own.
My intention is to live nearer my family as I do not have any family or friends near me where I live now. I applied to the other council quite a while back and I've just received an offer of a flat in sheltered housing near my family.

I receive state pension and I also receive PIP standard daily living and enhanced mobility.
Will moving into sheltered housing with another council affect my PIP?

The weekly rent is a little higher to where I am living now. There are extra payments to pay such as warden service charge, management service charge and city wide alarm charge which I know I will have to pay separate from the rent.
But how will my housing rent/council tax benefits be affected going to a different council?
TIA

Thank you Gordon for your quick reply, I really appreciate it.
My other concern is will moving into sheltered housing affect my PIP daily living.
In the past I have heard of some instances where the DWP have classed sheltered housing in the same category as a care home even though there are great differences, and the daily living part of PIP had been taken away from people that had moved into sheltered housing.
I just wanted to know if that's the case or not, and to know what to expect

Thank you Gordon for your quick reply

I have read somewhere that the DWP has sometimes mistaken sheltered housing with care homes

I was wondering if I would lose my daily living part of my PIP if I moved into sheltered housing ?