Why is 2-fluorobenzoic acid more acidic than 4-fluorobenzoic acid despite its intramolecular hydrogen bonding?
You seem to be asking the question &quot;Why does this intramolecular hydrogen bonding not cause a considerable effect to the $\mathrm pK_\mathrm a$ values of these compounds?&quot;


TL;DR That is because this type of bonding is only present in a specific conformer only and this type of conformer of the compound 2-fluorobenzoic acid exists in low population levels, 2%$^{[1]}$ to not affect the ${\mathrm pK_\mathrm a}$ of the compound considerably.

Regarding the conformers of the 2-FluoroBenzoic Acid


A throughout conformational search on the B3LYP/6-311++G(d,p) potential energy surfaces of the
studied molecules (the mono- and di- ortho fluoro- or/and chloro- substituted benzoic acids, plus the
parent benzoic acid, for completeness) was undertaken. The identified conformers are presented$^{[2]}$

Here both the cis conformers are planar and low energy while only one trans conformer is planar while both of them are relatively high energy of which Trans II is of relatively lower energy.

The two cis conformers have rather similar energies, with cis-II (where
the fluoro-substituent stays the same side of the molecule as the acid oxygen atom and a C-H . . . O=
stabilizing interaction exists), being the most stable form. The cis-I conformer has a relative energy of
2.82 kJ·mol−1
. In this conformer, the C-H . . . O= interaction present in cis-II is replaced by a weaker
stabilizing C-H . . . OH interaction. The C-H . . . O= interaction is more efficient in stabilizing cis-II than
the C-H . . . OH interaction in stabilizing cis-I due to the more favorable localization of the interacting
carbonyl oxygen lone electron pair, which stays in the molecular plane, whereas in cis-I both lone
electron pairs of the acid oxygen atom are out of the molecular plane. On the other hand, the interactions
between the fluoro-substituent and the oxygen atoms, which are of repulsive nature, also favor a lower
energy for cis-II compared to cis-I. This can be rationalized in similar terms as for the interactions
involving the ortho hydrogen atom discussed above. In cis-I, the F . . . O= repulsion is stronger than the
F
. . . OH repulsion in cis-II because the interacting lone electron pair of the carbonyl oxygen atom is in
the same plane as the fluorine atom in the former conformer, while the lone electron pairs of the acid
oxygen atom in cis-II are both out of the plane in relation to the fluoro-substituent.$^{[2]}$

  
It is important to note that though the population level of Trans II are low, it is still a stable compound and nevertheless has been detected.$^{[3]}$  

So.. Why is 2-fluorobenzoic acid more acidic than 4-fluorobenzoic acid?

I could not find any research for this but I could make an educated guess that the acidity of 2-fluorobenzoic acid comes from the similar stabilization as that in salicylic acid.$^{[4]}$ in the conformer cis II as shown below:-


References:

Kuş, N.; Fausto, R. Effects of the matrix and intramolecular interactions on the stability of the higher-energy conformers of 2-fluorobenzoic acid. J. Chem. Phys. 2017, 146 (12), 124305. [DOI: 10.1063/1.4978794]
(https://doi.org/10.1063/1.4978794).
Ogruc Ildiz, G.; Fausto, R. Structural Aspects of the Ortho Chloro- and Fluoro- Substituted Benzoic Acids: Implications on Chemical Properties. Molecules 2020, 25 (21), 4908. DOI: 10.3390/molecules25214908.
Daly, A. M.; Carey, S. J.; Pejlovas, A. M.; Li, K.; Kang, L.; Kukolich, S. G. Gas phase measurements of mono-fluoro-benzoic acids and the dimer of 3-fluoro-benzoic acid. J. Chem. Phys. 2015, 142 (14), 144303. DOI: 10.1063/1.4917031.
Dunn, G. E.; Penner, T. L. Effect of intramolecular hydrogen bonding on the relative acidities of substituted salicylic acids in benzene solution. Can. J. Chem. 1967, 45 (14), 1699–1706. DOI: 10.1139/v67-274.