Is there any way to see swim pool lengths details directly in the app instead only in the web app?
Right now I can only see the whole interval, but not each individual length and what style I swam in it.
If you mean the equivalent of the graphical lap splits of the intervals, as shown below, then there is no such equivalent in the app. However, the app will show you the stats (times, pace, strokes, ...) of individual intervals. So if you need to see the stats for each pool length, then just tag all the pool length as Intervals with the lap button, and they will be then listed on the Laps tab of the activity on the phone app.

I was looking more for the table view, you can see in the web app, that can be expanded to se the length details.
I don't understand why that isn' also visible in the app since they have the data and it would be so easy to implement.
Having the graphs is great but you can' see a simple table view of all lengths.

In the web you have shown the break-down of the intervals. The break down is (currently) not available on the app. As I wrote, if you need individual stats for each pool length on the app, you'd have to tag each pool length as an Interval with the Lap button.
Ok, so the answer is NO. Laps aren't the same thing as individual lengths and I don't understand why Garmin doesn't show it in the app. It's like only showing the total run distance instead of a break down by kilometres. I would understood if they didn't have the data, but they do as the web app clearly shows.
I know it does and that I can. That unfortunatelly doesn't explain why it's missing even after all the years it has been available. Seems like the mobile apps are just an afterthought for Garmin, always lagging behind in features and looking the same for years...
Yes, the app is always just a smaller poorer sibling of the web app, which is the main interface. Certainly also because there are in fact two apps that need to be developed on completely different platforms, they need to be kept in sync, and maintained - iOS and Android. There are also more important limitations in regard of the storage, memory, cpu, resolution, and permissions, on the phones, so keeping the functionality limited in comparison to the web app on a computer, is often the necessity.
It is often so with many similar services (for example Strava comes to the mind), since the web development is easier, and unlike the apps, it concerns all users, hence the main focus is on it, and it probably will stay so for some time.
As a software developer myself I understand those dificulties but also know that their just excuses. Company of this size with such a high focus on mobile devices shouldn pay bigger focus on their apps.
Especially when for absolute majority of their user base the mobile apps are what they use to access their data. Having all available only on a website is something that would be excusable 10 years ago but not in 2022.
I love their devices and my Epix but that doesn't stop me from expecting more from them as a customer.