Senior engineer sounds about right.
How many years of experience do you have (both in total and in this org/position)? Also, can you estimate how much value you've brought to the org? Example: if the web app you wrote was not made, what would the loss be?
Yeah, Senior Software Engineer is a good match then.
Works about right for the workload, responsibilities and the YOE.
The reason I asked about the impact/value is that it's a good way to argue your case. If you can quantify 'x' hours of manual effort (and the estimate should be an average person doing the work, not the best case), then you can start arguing using these numbers to show that you bring value to the org.
While it sounds like your supervisor seems to be pretty solid, it's possible you'll eventually sit down with someone esle who'll be deciding the final 'value' of your effort and would have a vested interest in paying as little as possible. For that conversation, whenever it may happen, you need to be fully prepared. That's going to involve hard number. Effort saved, value created, costs saved etc. It's difficult, but it's a useful dataset to have.
I've worked in smaller orgs like this in the past, and it's occasionally an uphill battle to get paid commiserate to the value you bring to the table. It's a good reminder for management that you're not easily replaceable and that they need to kep you interested enough that you don't wander off.