Recommendations for a new study area

Question

Edit: I am not asking about "which course to take" or "which career path to follow". I am asking which areas of mathematics were found interesting by those that share my interests. This goes beyond practical purposes as it also has the potential to provide insight into the process of doing mathematics, which oftentimes involves comparing the overarching "ideas" of different fields of study.

I just finished my undergraduate degree in physics, which included some core mathematics modules, namely

1. Topology
2. Algebra (group and ring theory)
3. Real analysis
4. Functional analysis
5. Category theory

I have found that most of my (what I consider to be) interesting mathematical discoveries come about by actively engaging with a good textbook, and attempting the problems therein. I want to do more mathematical research, but I am not sure which areas of mathematics are suited to me. Instead of giving them all a try (which seems borderline impossible to do thoroughly) I had the idea of describing the maths that I find interesting, and asking the community which areas they think I might find most fruitful to study. So below is a summary of the kind of maths I find interesting:

1. I enjoy being able to solve a problem visually, that is, I prefer visualising constructions and building intuition this way, before sitting down with pen and paper.

2. I enjoy proofs that are elegant, and do not involve excessive case analysis.

3. I enjoy the process of abstracting a certain notion as far as is possible whilst still retaining the essential properties.

These are very vague, so I provide below an example of a recent inquiry that brought me satisfaction:

I identified a new class of metric spaces which shared some properties with complex vector spaces, and investigated whether or not members of this class had certain properties such as path connectedness, completeness, and the compactness of closed balls.

To further aid the selection process, here are some things that I am bad at, or don't enjoy:

1. Almost anything related to analytic number theory.
2. Problems for which it is very difficult to attach a visual interpretation.
3. Calculus/applied math style problems.
4. Questions which seem overly specific, and do not make any attempt to be generalisable.

Here are a few more examples of mathematical facts that I found extremely satisfying:

1. Birkoff's theorem
2. The connection between $C^*$ algebras and compact Haussdorf spaces
3. The implication of Zorn's Lemma from AC
4. The Cantor-Bernstein-Schroëder theorem

I realise that it is difficult to guess what someone would find interesting, but my hope is that there is someone else with interests that align significantly with mine, and that they can simply add to the list those topics which they found interesting. It is important to note that I am looking for areas of mathematics which do not appear in my first list. I.e. something which I have had little to no exposure to before, as I am also interested in learning the skill of teaching myself a certain topic.