I found this question while trying to add some information to one of my previous answers.
Since the question was asked, bike design in general may have become more accommodating of female riders, and of smaller riders more generally.
As a smaller male rider, lever reach was an issue I dealt with as well, although my problem was more reaching the brake lever and shifting in the drops. In any case, since the question was asked, Shimano and SRAM now both have lever reach adjustment built in to many of their shifters. I have personally inspected current-generation Shimano Tiagra (4700) rim brake and Ultegra rim and disc brake levers (R8000), and one can adjust the lever considerably closer to the bar, or further away if that is one's goal. With Shimano and SRAM levers, the adjustment is done with an allen bolt, so it is continuous. This would improve the reach to the brake lever from both the hoods and drops.
In addition, Shimano makes the 105-level ST-R7025 hydraulic disc brake STI lever and a Tiagra-level unit, which are smaller than the regular one-size fits all STI units. Unfortunately, no rim brake version is available, nor is this unit available in Ultegra or Dura Ace.
In this 2016 blog post, Georgena Terry (a mechanical engineer and framebuilder) said that it might be possible to increase the amount of adjustment on Shimano levers. She discussed how Isla Rowntree, a UK national cyclocross champion, replaced the reach adjustment bolt with a longer version. In the year the post was written, Shimano was on the 9000/6800/5800 series of components, i.e. one generation prior to the current one. It is likely that this hack would work in the current generation as the levers are nearly identical, but I have not tried this personally. At the time she wrote the post, the smaller versions of the Tiagra and 105 hydraulic STI levers weren't available.
I believe SRAM offers the same reach adjustment features as Shimano, but I can't confirm as I have personally not preferred to use SRAM. However, I recall that SRAM had built-in lever adjustment in the late 2000s, and I think they may have been the first to make this widespread. I do not believe they offer smaller versions of their shifters.
Disappointingly, Campagnolo have been late to embrace this type of adjustability. You could buy spacers to move their levers further away from the bars. However, the just previous generation 11s hydraulic levers have reach adjustment. This generation of rim brake levers do not. The current generation 12-speed levers offer reach adjustment for both hydraulic and rim braking. At the time of writing, they're only offered at the Chorus level or higher. For rim braking, the only adjustment appears to be a single fixed position that's closer to the bar. I have not inspected current-generation levers personally, so I am not sure how much closer they move.
Back to the original question, depending on the component specifications, entry level road bikes may have weaker brakes. If the OP's girlfriend had to squeeze the levers too hard, that could cause hand pain as well. For rim brakes, this can often be attributed to poorer pads, and one can often just change the pads for Kool Stops or a higher-level pad by the original manufacturer (e.g. get Shimano 105 or Ultegra pads). If the bike has mechanical disc brakes, as my wife's does, this is inherent to mechanical discs. Compressionless brake housing might improve things somewhat. If one does not want to upgrade the levers, one could search for cable-actuated hydraulic brakes, although this is probably about a US$200 upgrade. With many entry-level bikes, making significant component upgrades is not worth it, and one might as well sell the bike and get a better spec bike.
To the best of my knowledge, while few road cyclists truly need hydraulic disc brakes, they can produce a lot of braking force with very little lever input.