Excel ignoring part of formula

You want to use <=0.01 not =0.01 but if that 0.01 could be in either direction (45.01-45 OR 45-45.01) then you want ABS(F3-G3)<=0.01 and then you also don't need that additional F3=G3 statement.

You could also benefit from using IFS:

=IFS(F3="","",ABS(F3-G3)<=0.01,1,F3>G3,3,F3<G3,0)

by the way, the reason =0.01 probably didn't work is probably due to round off issues so although it shows as 0.01 that actual value may be 0.00999999999999 due to how decimals have to be represented.  In fact you might need to use <=0.011 just to be sure in case the roundoff is the other direction and it is 0.0100000000001 (BTW the number of decimal places I am showing was random and not adjusted to that actual resolution that excel stores)