I'm sure most of you are aware the the XE has been discontinued in the US market. On top of that, the P250 S was one-time vehicle available only during the year 2020.
I've had mine for 18 months now and I thought I should give comment about my experience so far even though it's likely to never return to the US market. For those of you across the pond in Europe, the XE is still available, but not the P250 S.
Honestly, you're not missing out on much, but I do really like the car.
Here's a list of my observations and opinions just in case you may decide to purchase a used one someday.

• The interior is great. I can't complain about it much at all. It's very attractive to the eye and has pretty much every feature that my 2017 XE was missing: lumbar support, folding rear seat, leather steering wheel, power adjustable steering wheel, larger display and more.
• I can't complain at all about the exterior. It's a sharp, fantastic looking car.
• The low-profile tires are great for handling, but they're loud and you feel every bump in the road. It's a sport sedan, so it makes sense to have low-profile tires, but the downside is noise and comfort.
• The engine has great power, but it's loud. I'm always hearing that little 4 cylinder. I think Jaguar could have done more to quiet the interior. The combination of engine noise and road noise is a bit unfortunate. It's kind of a noisy car.
• The eco assist that turns off the engine has stopped working at least twice. For whatever reason it fails for about a month and then starts working again. The dealership says that the codes need to be cleared out, but it does fix itself eventually without a trip to service. I understand that the eco assist is intelligent and it knows when it shouldn't be shutting down the engine, but this issue isn't a part of it's intelligence. It literally just stops working for weeks.
• The feature that reads speed limit signs and displays the speed limit on the dashboard will occasionally turn itself off. I have no idea why this happens and it's not like I'm doing it on accident. To turn it off you have to navigate through a couple pages of settings and uncheck the box. It's not something that can happen by accident.
• When I first purchased the vehicle, the electronic vent system in the grill was broken and making loud clicking noises when starting and turning off the engine. The dealership repaired it under warranty, but it was loud and annoying during the time it was broken. I guess it came off the assembly line that way. The car had only 22 miles on it when I bought it. Definitely a quality control issue.
• The weather stripping on all 4 doors failed during the first year. The dealership replaced the stripping under warranty. The tech told me that at some point during the assembly process, one of the factory workers had made an error with the stripping. The worker removed the stripping to correct the error, but didn't clean off the adhesive before installing the new stripping. This is why it came off on all 4 doors during the first year and it took almost 2 months for Jag to get the replacement stripping from Europe.
• All of the stations that were starred on the radio decided to unselect themselves the other day. I had to go through the entire FM broadcast and re-star all the stations I like.
• The blind spot monitor will occasionally fail. When it fails, an error message comes across the dash telling me "Okay to drive with caution. Blind spot monitor fault detected." It will then tell me that service is required. The next day it usually goes back to normal. This has happened about 5 times.
• If I get into the vehicle while it's running and put it in drive before the driver door is closed, I get an error message on the dashboard telling me how to properly apply the parking brake. I've never had this issue with any other car. For some reason when the door is open, the shifter will send a parking brake error message to the dashboard with a beeping sound if I try to put it in drive. This happens to me all the time at casinos and valets. I have an old habit of putting cars in drive quickly before closing the door.

So that's it. Other than a few, qwirky issues, it's really a fantastic car. I love pretty much everything about it. I always get compliments about it and catch people looking at it. If it were only a bit more quiet.

 

I have an XF with a 4 cylinder 2.0 Turbo. For some reason, I hear the engine when it's running but not loud at all when I am inside the car. On the highway, I felt like I'm driving an electric car., very quiet The only time when the engine gets loud is on initial start-up when the RPM is high but when the RPM goes down it's back to normal.
My XF does not have a Sport package nor it has AWD. It looks like your XE is a Sport, could be the reason why the engine is loud?

 

The XF probably just has better sound dampening technology because it's more expensive and available with a V6. Makes sense for Jag to make sure it's quieter.

 

One thing I forgot to mention in my OP is how lousy the remote system is.
I was at a casino tonight and forgot exactly where I parked, but I knew approximately where it was. I'm walking through the parking lot with the remote in my hand pressing down on the red hazard button over and over again but my car stays silent.
I then find my car but keep pressing down on the button as I get closer to it. I then get right up to my car, about 2 feet away from the trunk and it does not detect my remote. It was so irritating. I can't believe I was standing right at my car pressing that button over and over again only to have my car completely ignore it.

There's also the issue of my car not detecting the remote when it's in my pocket. I walk up to the car and grab the handle but it doesn't unlock. I guess my pants are too thick for it to detect my remote??
And when I sit in the car to start it, I get a message on the dashboard telling me to insert the remote into the dashboard, but my car does not have that feature. It's keyless entry and keyless start.
I took my remotes to the dealership last year for new batteries and it didn't change a thing.

 

What I do is press the panic button for 3 seconds & siren is activated. Press again for 3 seconds & panic button siren stops

 

I'm pretty sure I tried everything during my angry attempts, but I'll give your suggestion a shot. Thank you!

 

Your problem sounds more likely to be the remote. Did they put in an old battery?? I have never had it not unlock as I put my hand on the door handle. And the remote lock/unlock works at a pretty good distance. Maybe check the remote battery's voltage?

 

Bought the car brand new in November 2020. Remotes should be good. Had new batteries installed in both remotes at the dealership last year.