How to install a GFCI?
Multi Wire Branch Circuit
You have an MWBC. It provides 2x the power with 1.5x the wires (3 wires instead of 4). The catch is:

If wired to a typical double-receptacle, you need to remove the tab for it to work properly
Neutral (white) must be wired in a way that removing a device from the circuit won't affect other devices
Must have a double-breaker or handle-tied breaker

Your old setup has all of that. What it doesn't have is GFCI protection. While with an ordinary single circuit, you can install GFCI at the point of use (a combination GFCI/receptacle) or in the panel, with an MWBC the usual solution is in the panel. You do actually have an alternative, but it is more work and only makes sense if you also want to have more receptacles:

Replace this receptacle with a combination GFCI/receptacle. Do not remove the tab. Connect black to hot, white to a pigtail to neutral.
Add a new combination GFCI/receptacle in another location (could be another box right next to this one or could be on the other side of the garage, whatever you want). Do not remove the tab. Run a new cable 14/2 (or 12/2 is OK) and connect the existing red wire to the black wire of the new cable and connect the white wire of the new cable to the old white/pigtail (i.e., don't chain it through the receptacle). Then wire up the new receptacle standard black/hot, white/neutral.

That will essentially split the MWBC into two separate circuits, each of which can handle a full 15A load. If you want to use two large tools in one place and nothing else, then the existing receptacles (plus GFCI in the panel for safety) makes sense. But having 4 receptacles (2 on each of 2 circuits) can be very useful.