“Personal Item” under seat bag

only if its half empty. The space is not 40L big.

First, everything depends on the specific airline you will be flying, since there is no universal standard across all airlines - you always need to look up what the limits for baggage are for that specific airline you will be flying (there are limits for all kinds of baggage: checked, carry-on or "small personal item"; these limits can be found pretty easily on every airline's website, and you either need to understand them and follow them, or just hope you get lucky but be prepared to accept the consequences if you are not - the consequences may be expensive).

Second, your question is about a bag which you describe based on its volume. No airline cares about any bag's volume (there's no way to accurately measure interior volume and they really don't care how many pingpong balls or other objects you could stuff into a bag). They care about one or maybe two things: the bag's dimensions – specifically its exterior dimensions (height, width, depth, and maybe it's combined H+W+L) including any handles, wheels, bumps or protrusions; and (sometimes but not always) the bag's weight (with all your stuff packed inside). These are the things they can and do measure.

The "space under the seat in front of you" is quite limited, but varies significantly based on type of aircraft and other variables that are nearly impossible to accurately predict. Most airlines assume your "small personal item" will go under that seat, and your "carry-on" bag (often referred to by European airlines as "cabin baggage" or sometimes "hand baggage") is expected to go in the overhead bin. Some airlines (typically low-cost airlines) actively police bag placement, others don't care much once you get things on the plane, almost all of the bag scrutiny and enforcement of baggage limits/rules will take place at check-in or the boarding gate (or both).

If you are hoping to only get by with a bag that fits under the seat, you need to do the research to find out exactly what the limits are (dimensions and possibly also weight limits, though that's uncommon) and be prepared to live with those limits. Frankly, there's very little space under that seat on most planes.

Here's an earlier thread about living within the limits for carry-on bags and "small personal items" which you may find helpful - but remember, you need to know what the limits are for YOUR flights, do not assume that any other limits you read about or previously experienced elsewhere make any difference - they don't. It's all about what the limits are for your specific flight.

Seeking "Personal item" bag rec for Lufthansa

I have one of those RS backpacks. I think it falls into the carryon in the overhead category, I don’t think it would fit under seat. Even just partially filled, it has enough structure that it would probably be larger than the under seat area. The measurements aren’t under seat compliant for any airlines that I know of.

Rick’s 40L backpack suitcase

You mean one of these or something else?

https://store.ricksteves.com/shop/p/classic-backpack
https://store.ricksteves.com/shop/p/carry-on-backpack

If it is one of those, or something like it, I join with those who say putting it under the seat is unlikely.( unless it is empty to the point that it is essentially useless)

Are you also traveling with a carry on, plus that 40L bag? That sure is pushing the limits. That being said, it seem very common for people to do so. Having a carryon and a “personal item” that must have every personal thing imaginable in it because it often is at least as large as a carry on.