Renovate/renew linoleum flooring and vinyl floor tiles

Hello dear house-building community,
I need advice on floor renovation in a 60s newly built apartment. I am an amateur and have just been reading up a bit, but this has raised almost even more questions.
I have already searched the forum for answers but haven’t quite found what I’m looking for.

I want to renovate (beautify) the floor, which is otherwise in good condition, because the colors are no longer nice. (Only in the hallway are some vinyl tiles missing). The apartment is currently unfurnished and afterwards I want to rent it out. The renovation costs should be kept low because the rent index in the area is low and I will hardly be able to recoup high renovation costs, but of course it should not be a botched job!

I have a linoleum floor in the kitchen, a vinyl floor in the hallway and WC (fully glued).
My idea would be to lay a CV covering loosely over both floors, i.e., fix it with tape.

[*]My planned approach:

[*]With the doors, another layer of CV covering will fit
[*]I clean the floor and make sure it is even
[*]Then I simply lay the CV covering on, as shown in YouTube videos

Is it really that simple, or am I forgetting something?
(sound insulation, vapor barrier, can I use any double-sided carpet/floor tape, etc.)?

[*]What do you think of my idea? How would you approach my goal of a cost-effective floor renovation?

Attached are some photos.

I am really looking forward to your suggestions and opinions.

You can deep clean the linoleum floor and then polish it - then it looks like new. We have done this several times at our place. Of course, this only works if it doesn’t have any holes or anything. If it has come loose somewhere, you can simply re-glue it.

Just to be cautious, since the timing also fits very well. With the vinyl flooring, one should be sure that it is not Floor Flex panels, which contain asbestos. These were often installed at the time, and purely visually it could quite possibly fit, so caution is advised.

You can deep clean the linoleum floor and then polish it - then it looks like new. We have done this several times at our place. Of course, this only works if there are no holes or anything. If it has come loose somewhere, you can simply glue it again.

Thank you very much for the tip! It's definitely an option.