Short answer: you probably don't need the degree for most jobs. As is usually the case with these answers, being conversant with the topic at a professional level, having a portfolio of high-quality work, and (to a lesser extent) having certifications can probably deliver the most of the same information that holding a degree would. There is some variation by field as well-- a smidge of technical "data analytic" knowledge complemented by other knowledge is sometimes ideal (I work in health care analytics, and clinical experience is an absolutely huge advantage to have when poring over reams of data).
However, even if you are capable of doing the job, it may be a mistake to assume that your skills are equivalent to those that you would have if you had the degree. It sounds to me like you're open to always sharpening your skills, which is awesome. If you want to move into analytics for your career, make sure to retain that attitude and constantly watch out for arrogance. It's extremely easy to wind up in a situation where you perceive your understanding to be more complete than it is (it's a constant issue for me, and I both work in this field and also have the quantitative-skill-degree background). There is just a huge amount of information to know.
Anyways, my advice is to focus far, far less on titles and qualifications and more on the work. What you're called on your business card is mostly unimportant. What you can do with data of the type your employer has, and on the scale that they have it, is supremely important. You will probably be a great fit for many roles in this space, and a terrible fit for many roles as well.
"Analytics" is deep in buzzword territory at the moment, and so you can probably sell yourself successfully without the degree. That also causes a few difficulties for you:
There is no way of knowing in advance how much the person you report to understands the subject matter. This is double-edged-- a superior who doesn't know enough to catch you out in something that "everyone" with a related degree would know won't catch you being "underqualified", but they also won't be able to correct you when you err or teach you more.
A lot of people who want work products that would fit well under "analytics" don't really understand what they want, how to use what they want if they were to get it, and, crucially, what limitations exist on what can be known/done with what they want. This is, in my opinion, the area in which formal education is the most useful-- you would have that background knowledge to add. It's always hard to estimate what you don't know, but that risk can be a lot more acute when you are mostly self-taught.
There are a ton of people with positions and titles like this, with huge variation in quality among them. Some people are awesome at throwing together reports in PowerBI or Tableau, but understand essentially nothing about the underlying concepts and so are likely to make lots of errors, sometimes very consequential ones, outside of routine work planned and supervised by more knowledgeable people. The risk of this varies with specific responsibilities associated with specific jobs (i.e., if data visualization is your assigned role, it may not matter that you don't understand intricate details of logit regressions; the converse can also be true).
"On the job" training works well for some areas and some people, and very poorly for others. You can pick up a lot of SQL coding skill while working, because you can often test your queries at intermediate stages and validate against fixed, external information. That's less the case when you're relying on a 3rd party library to run elastic net regressions (learning all of the underlying concepts from scratch is probably not what you were hired to do on the clock).
A quantitative-field-focused degree suggests a lot about what skills you have, and what knowledge you can tap. A CV entry listing "data analyst" does not. It's just too broad of a title for every job featuring it to be directly comparable.
On the other hand, there are plenty of people with applicable degrees that have middling applicable skills at best. You are extremely unlikely to be anywhere near the least competent person making a living doing this sort of work.