LAMBDA( value; value) isn't a identity function

The formula

 =SPLIT("1\10/10\00002.2";"\")

doesn't result equal to

 =MAP(SPLIT("1\10/10\00002.2";"\"); LAMBDA(v; v))

At the former, implicity conversion is inhibited; the latter, it takes place.

Why? Is there a way to control this?

To ensure that the result of the formula returns each part as text, use TO_TEXT:

=ArrayFormula(MAP(TO_TEXT(SPLIT("1\10/10\00002.2";"\")), LAMBDA(v; v)))

This will return

I have tested the above using United States, Uruguay and France as the spreadsheet locale.

Alternative

If you need to get 0002.2 instead of 2.2, add a ' before 00002.2. Depending on your specific use case, the most straightforward approach might be to add it manually or use a formula.

Formula example:

=MAP(SPLIT(SUBSTITUTE("\" &"1\10/10\00002.2", "\", "\'"),"\"), LAMBDA(v,v))