Aero Blaze 3 GORE-TEX

I love shoes. So allow me to get a little carried away for a minute. Anyway, trail shoes are less likely to be bouncy like road shoes because they're more designed to prioritize stability and durability. I'm exclusively a road runner, but when it's winter I do rotate in some trail shoes with lower lugs for the snow and sleet. The closest I've found that are less firm and more cushioned and a little bit bouncy (but nothing crazy)... Nike Pegasus Trail GTX 4 or 5. Hoka Clifton 9 GTX are cushioned weatherized road shoes - not really bouncy but definitely cushioned. Saucony Triumph 21 also has a storm shield version or something like that. The foam is a cushioned TPU. You could probably do some light trails with it. And finally, Salomon Aero Blaze 3 comes in a GTX model - same bouncy foam as the Aero Glide 3 with a reinforced outer sole for light gravel trails and the protection of Gore-Tex. It's fun for a winter shoe. I think you could pull it off on packed dirt. Finally, I'm waiting for a pair of Hoka Speedgoat GTX spikes that are designed for snowy and icy trails. Not sure that you'll get bouncy energy return from those though!

Currently using Salomon Aero Blaze 3 gtx. They've been decent, but having some grip issues uphill on compacted snow.

Both Asics gortex and Salomon gortex Ive found to be the best I've used.   I get probably 2-3000km out of them?   Say 8km a day of sandstone gravel fire trails and rocky escarpments for a year. I  would get 12-18 months out of them.   Sometimes I just wear out heel rubber and foam is still good so I build it back up using Sikaflex or something to go another 6 month lol 

I have the Catamount 2 and I really like it (ran in them today), but actually prefer the Cascadia. Also, another vote for skipping GTX. You probably don't need it (or want it) for most runs.

Massive hiker here. Noticed you asked for a shoe and not a boot. I understand this choice for a single buy. My favorite hiking shoes are the Salomon GTX or similar. There are a lot of models, so if you can try some on that'll fine-tune your personal preference. But this shoe hits my feet and ankles comfortably, AND has a wicked tread for the thousands of rocks it'll be bumping over on Phoenix and AZ trails. Hint for affordability: if you get your size in a brand, I often find that reputable merchants on a large online auction site sell NEW hikers at a bit of a discount. Runnerup brands would be On Cloud and La Sportiva. ymmv (literally) of course

I have a pair of 4 year old Goretex Salomons that are still waterproof despite the age and lack of care (never really cleaned aside from spraying off dirt), so might be a technical defect if the puddle never got past the tongue of the shoe to let water in (if it has no gusseted tongue). Though that is quite coincidental and unlucky you went through 2 brands/shoes like this. I'm also not familiar with La Sportiva since I mostly buy Salomon, but that material looks like mesh to me. I've never seen a pair of Goretex shoes with that kind of material.

I used to rock a pair of GTX trail runners from Solomon during walnut harvest... They stopped making them (boo), and I couldn't find any existing pairs that weren't stupid-overpriced. I went on a deep dive and tried every GTX model from Solomon, hoping for a replacement. They all fit differently. It was infuriating. So, a warning to all: Try all models of a given brand, because you can't rely on equivalent fit. I currently rock a pair of Altra lone peaks in blue for travel shoes, and they're the only shoes I've bought where I did not have to replace the insoles with my Soles. I was blown away.