There are two semi-independent clotting systems.
Broadly, aspirin works on the one associated with heart attacks. Most strokes are caused by the other. So taking aspirin for strokes doesn't usually help. (Source: had a mild stroke, was told this by multiple neurologists.)
Covid seems related to both.
You need non-trivial blood thinners - Warfarin, rivaroxaban, apixaban - to affect DVT etc, and those are high-maintenance meds with side effects of their own.
But there is some evidence that aspirin does help with Covid clotting, and low doses for short periods seem pretty safe.
So the worst you'll do is improve your odds of avoiding problems from something that's already not much of an issue.