Run filter in each row dynamically - google-sheets

Question

I'm trying to manage a dynamic set of data over the course of several steps, and at each step I need to remove a specific value from each row, and shift the remaining values to the left to fill in any blanks.
I know I can use
=arrayformula(if(range=value, "", range))
to remove the specific value, but I've only been able to find
=filter(row, row<>"")
to fill in the blanks, but since the number of rows changes, this isn't going to work.
Edit:
I want to turn something like this
Column A
Column B
Column C
Data A1
Data B1
Data C1
Data A2
Data B2
Data C2
Data A3
Data B3
Data C3
Data A4
Data B4
Data C4
etc
etc
etc
to this
Column A
Column B
Column C
Data A1
Data C1
Data A2
Data B2
Data C2
Data B3
Data C3
Data C4
etc
etc
etc
Since I only know how many columns there are, I can only pre-set the formula to filter each column, which moves data vertically. I want to move it horizontally, but where the number of rows is variable, I can't manually pre-set each row to use filter.

Answer 1

Solution: applying FILTER() in combination with BYROW(). Because Google's BYROW() is unfortunately limited to a single value return from it's LAMBDA(), we have to rely on the old ARRAYFORMULA/JOIN/SPLIT trick.
=arrayformula(
split(
byrow(A1:C4,
lambda(row,
ifna(
join(",",
filter(row, row<>"A")),
""))),
","))

Answer 2

As of today (23-Jan-2023), it appears that Google has updated the BYROW/BYCOL functions to allow the return of an array result per row/column, so the answer to the OPs question could now simply be =byrow(range,lambda(row,filter(row,row<>""))).
I have not seen this documented anywhere, and the help pages for the BYROW & BYCOL functions still state that only a single value per row/column is allowed.
Slightly off-topic, but I can also confirm that you can pass the individual row/columns from a BYROW/BYCOL into the other LHFs as well (e.g. a SCAN within a BYROW to give a row-wise running total, etc.)