Question about potential career path (Technical Account Manager)

I'm currently a Technical account manager at a company and I'm uncertain where to go from here. I currently make 150k, with some of my more experienced coworkers making 200k. I'd like to apply to other companies to make more money.

But I'm wondering, is staying in this sort of role good long term?

Some additional information on what I do, since I understand this role varies company by company:

We interact a lot with clients post sales making technical recommendations on the products of ours to use.

We sometimes help direct clients with integration, or do it ourselves which involves using our REST API.

We also sometimes have to configure and customize our web application front end, which involves making changes to its HTML, CSS, and JavaScript.

We would sometimes also need to investigate and deploy bug fixes for production.

Now, looking at potential jobs, I'm seeing Technical Account manager, Solutions Engineer, and customer engineer roles that seem really similar to what I'm doing now, paying about 150k average, maybe even a bit more. I'm uncertain what kind of progression there is though.

On the other hand, as a software engineer (which,despite having a degree in CS, i have no work experience doing, other than what I'm doing now), it feels like there's an, obvious to me, career progression. The issue is that it appears that the average pay for what I think I could work as (junior/entry level software engineer) is closer to 100 - 120k.

Should I keep trying to stay in my current job type? What sort of new positions should I aim for to make more money?

Should I bite the bullet and go into software engineering, losing some short term income in exchange for a better career path with better pay in the future? Should I be applying for entry level positions? or staff/intermediate level Software engineering roles?

any advice is appreciated!