I think it's just a personal preference! Honestly, I've tried lots of different ways.
Come cleaning time, I actually really miss my 600 sq. ft. apartment with all cheap surfaces

. Back then, I would clean each room in total- there were only 4 (bedroom, kitchen, bathroom, living room) and each one would take 15-20 minutes. I used to clean on Sundays while doing laundry- the washer/dryer was in a closet in my bedroom- so that was really easy too!
Cleaning my townhouse top to bottom is a 4-5 hour job. Cleaning the whole thing weekly obviously did not last. I've tried so many things since moving here:
1) Every other weekend, cleaning the upstairs on Saturday and downstairs/main floor on Sunday. Felt like I was then spending my weekend on cleaning.
2) Every 2-3 weeks it all on the same day and splitting the house into four "zones" with each one progressively being a smaller amount of work- zone 1 upstairs bedrooms and bathrooms, zone 2- living room and vacuuming the stairs (2 sets) themselves zone 3- dining room and downstairs bathroom zone 4- kitchen.
3) Your second option there- going around and dusting the whole house, cleaning the surfaces, then vacuuming, etc.
What I do currently:
During covid stay at home, I realized I was much happier doing jobs as they looked like they needed it, rather than cleaning all at once. I always thought I'd hate this, but given the amount of time it takes to clean my place all at once, I like it much better. The house still looks reasonably clean all of the time. I realized I didn't necessarily need to clean the whole house just because the toilets needed it, or just because things were looking dusty.
So just a couple of days ago I got out the "carpet vacuum" and vacuumed the living room rug, living room furniture, and the most-used set of stairs. That's all I did because that's all that was noticeably dirty.
Another day I might just dust all of the furniture if it's looking noticeably dusty. Or I'll go around and do the mirrors/sinks and toilets in the bathroom. Or get out the actual broom and just sweep the wood floors.
It doesn't feel so painful that way. The one thing having a bigger house DID help me with is clutter. One, I have way more storage. Two, actually going upstairs for bed got me in the routine of picking up the main floor every night before I went up. Every night before I bed, I pick up any clutter down here. Since I keep up with it, it takes 2-3 minutes at most.
Sometimes I get too busy or lazy and let it all go way too long, and then find myself in a place where I have to just do the "big clean" all at once. But that's maybe every 2 months or so.