Hi
That has been one of my doubts about George of 53 Manchester Street. It was quite a large family that he had, and if the Browns were joined up with it then probably you, or someone you know, would have had some knowledge of that fact (even if you didn't know exactly which family it was)
The 1921 census should be released in early 2022. It will be only on findmypast, and I expect that initially it will be some kind of pay per view and not included in their subs.
The 1931 census was sadly lost in a fire in WW2 (not as a result of enemy action, which somehow seems to make it worse)
I was going to say that we don't have any Salford electoral registers online, but in fact I now realise we do - on findmypast again. The answer may be there! I don't have access

Live as it happens!
Salford South Division is I think what we need. Loads of Annie Marsdens in the free index, which you can see if you are at least registered as a free member (like me!)
https://search.findmypast.co.uk/search-world-Records/england-and-wales-electoral-registers-1920-1932No way to tell who they are from the index.
There is another database on there, England & Wales, Electoral Registers 1832-1932. On this there are no names given in the results pages, and instead you get a link to the image. In the past it has picked up anything on the page (transcribed via optical character recognition I guess), so look for John Smith, and you not only get all of them, but any page hit where there is a John, and also a Smith on it. Not good!
It could be manipulated via quotation marks, keywords, and comparing the image number, but they seem to have taken the image numbers away.
Entering "Marsden George" in the surname box, and "Manchester Street" in the keyword box, it tells me there are no results. Taking off the quotation marks and it then says 28 results (but is it still reliable then?)
Put the quotations back, and forcing it against its will to give me some results (I mean click on no results) and there are actually
6.
Two for 1918, three for 1919 (spring and autumn) and one for 1923
I think there may be an extra George in there, son George William perhaps?
Then looking for "Marsden Annie" and "Manchester Street", there are 4 results (1918, 1919 x 2, spring and autumn, and 1923.
That makes sense with two electoral registers per year for a while from 1919. And it's picked her up for the same years. Encouraging.
Theoretically it means that there should be an Annie Marsden on a page where the OCR text machine has also picked up Manchester Street. But without seeing it I can't be 100% sure of course.
The 1920-32 database, better transcribed, no doubt will pick them up in every year wherever they were!
But using the keywords on the other one gives us hope that there was an Annie with George in Manchester Street.
They also have the 1933 Manchester + Salford directory on there, so a bit later than the one on ancestry. Again when you search the index the results give no names, only a link to an image.
EDIT Deleted the last bit, got it wrong!
John