SN1 Reaction Involving Carboxylic Acids Which oxygen atom is more nucleophilic in carboxylic acids?

If we look at this page, it says the carbonyl oxygen is more nucleophilic:

However, I also learned in class that $\mathrm{sp^3}$ atoms are more reactive than $\mathrm{sp^2}$ atoms.

So, in an $\mathrm{S_n1}$ reaction where the solvent is acetic acid, which oxygen attacks?
The carbonyl oxygen is more nucleophilic. You can draw a resonance structure of the carboxylic acid that places a formal negative charge on that oxygen which rationalizes its greater nucleophilicity. Also, after it adds to the carbocation, the resulting intermediate will be resonance stabilized. If the other oxygen attacked, no resonance structures would be possible.