TL;DR It will work fine
Your freezer runs on a 15A or 20A circuit. But it only uses 2.5A, which is much less than 15A and also much less than 13A. It might use a little more when the compressor starts up, but only for a few seconds, which is not a serious concern.
A "home warranty" usually doesn't mean much, and in many cases they will use any excuse to exclude something from coverage. In this case, that would probably not be "13A extension cord" but "any extension cord". Why? Because your freezer instructions probably say "do not use an extension cord".
From a practical standpoint, what matters is why do they say "do not use an extension cord". The main issues are:
- Can it handle the load? That is a real issue for some things, but should not be an issue here (2.5A being much smaller than 13A)
- Is it safe in other ways? The big ones are: tripping hazard and potential damage to the extension cord. If you run the cord along a wall then there is generally not much of an issue. If you run the cord across the floor then these are both big issues. You have a tripping hazard if the cord is exposed and a hidden damage concern if the cord is covered up.
So if you are using the extension cord in a safe manner then this really not a problem. Moving the freezer to the garage may be a much bigger problem. Ordinary residential refrigerators and freezers are designed to work well in a narrow temperature range - e.g., between 50F and 90F. If you install them in a garage that has wide temperature swings (both cold and hot are concerns) then they may not work properly.