Photochromic sunglasses - yes or no?

My bilateral cataract surgery is sked for Mar 9 and I'm going with distant vision lenses so, for the first time in my life, I have choices in sunglasses other than cheap clip-ons or expensive prescription ones. I know I want polarized, thinking about photochromic as well but I have questions about how well/quickly they react to intensity changes?

A lot of my rides involve going thru underpasses, changing from bright to dark with a bright glare on the other end. These are often home to homeless folks; they mostly stay out of the way but there are some who wander around. In addition there's sometimes debris on the path and ice in winter. I'm forced to slow way down, even with headlight on, for safety - and even then my eyes are slow to adapt behind my current dark gray sunglasses.

Anyone have experience with photochromic lenses? Will they switch fast enough to give me safe vision? Or am I seeking a unicorn, and should just learn to live with it?

It's really hard to say as diminishing eyesight is such a personal thing.
Lately I find it harder and harder to drive a car at night to give you a reference point.
So then it depends where and when you ride. For this reason I have a few different pairs
For bright sunny days around an urban area - sunglasses
For bright sunny days on a trail with a lot of transition from bright sun to heavily shaded - I prefer Photochromic. Yes they don't get as dark as sunglasses or transition instantaneously but I find seeing more of a problem in the shaded areas than in bright sun. So not being as dark but still providing some glare block I find most helpful.
For dusk and dawn - I prefer yellow tinted night driving glasses. Things seem brighter and clearer.

This said I'm contemplating something with interchangeable lenses that is easier to carry than multiple pairs.
I've seen these that offer a Photochromic lens in the kit, but it seems they're all sold out at the moment
In my backcountry snow years in MT and ID I wore Vuarnet Skilynx. In later years I had Opticus make glasses. I find I too need several different lenses. 4-8% available light for snow and glacier(ice) use. And 50% for motoring around Minnesota in summer. I gave up on transitions too. Now ALL my lenses are tinted to 50% and some are polarized.

"Polarizing is NOT recommended where accurate judgement of surfaces and terrain is critical (jumping crevasses, hanging from ropes, high altitude mountaineering). Polarizing can cause some LCD displays to black out."
Regarding multiple glasses, what used to kick my butt was crewing on a sailboat. All that WHITE on a sunny day can blind you just like snow, but when adding the glare off the water made snow look like shade! Eventually, they were able to help me with transitional glasses, but they would never be clear. They started out pretty dark.... and went nearly black in the sun
I've had lens replacement done. Mostly for driving reasons I wear a good brand of polarized sunglasses in the summer and amber non polarized sunglasses the rest of the year and both work well for mountain biking... neither are RX though

Didn't care for photochromic for driving obviously but also to Bright seem like the trail looked washed out
I have a couple of cheaper photochromatic pairs that I started wearing on my motorcycle years ago. They are great for under a helmet since they are hard to adjust when riding, and my helmets have drop down sun visors built in if it gets to bright. With the visor down, they combine to work in the brightest conditions - although many photochromatics need UV to activate, so a premium UV blocking visor will reduce the effectiveness significantly. Cheap visors don't seem to matter as much.

On the bicycle, I wear them for all but the brightest midday sun where they just don't get dark enough (Maybe 60%). I keep some 88% Oakleys (polarized iridium) in my gear bag for those rides. The photochromatics are great though for morning/evening commutes and night riding where you just want some wind and debris protection. One of my pairs have a nice little removable foam ring for wind reduction behind the lenses which is great on the ebike for those cold morning rides. The Oakleys are tighter fitting wraps (Gas Cans or Valves).

I'm due to get some mild prescriptions for the first time every, so I plan to try out either the Transitions or NXT Varia photochromatics as the optician says they can get up to 80% dark tint and recover faster. For the "tunnel" scenarios, no typical or economy photochromatic I have seen has a fast enough recovery time to lighten in time to be useful. Most take maybe a minute to darken, and 5 minutes or more to fully lighten back to clear. They are very temperature sensitive too.

And economy photochromatics supposedly have a lifespan. It seems like most users say 5 years or so max, and they react less and less (and slower) after that. I have some 5+ yr old ones that do seem to be a little slower and lighter, so they just get relegated to safety glass duty in the garage.
Vaurnet Skilynx lenses were a major hit due to the tinting's ability to highlight details, like moguls. I found they also highlighted shades of green revealing details otherwise unseen without the Skilynx lenses. There was a PX2000 that worked well on water. The newest are stupidly expensive. So it's Opticus for me.