The way you describe it, the company you work for is giving you all you need to get started working. They're backing you and covering all the downside.
There are a number of factors that could influence whether this should be a separate legal entity.
First is how you access additional funding. If it's internal, then look at what house style is. If it's external, then you need a distinct company vehicle.
Second is how you will experience and cover risk. As a rule of thumb, the further you are from core business, the higher and more unfamiliar the risk. If, in order to pursue the business you have scented, you will be exposing the core business, they are likely to prefer you to be a distinct corporate entity, so that the maximum exposure is loss of their investment.
Third is the trade-off between cost and opportunity. Depending on your location, there may be significant opportunities for the company to offset some costs of new activities against tax, or to access grant funding. Sometimes this pushes against separation, sometimes towards. Get specialist support externally if this isn't an area the company already knows well.
Fourth is a view of the end game. If you are becoming the new product pipeline, it may add more complexity than benefit to spin out. If you are a way of helping the company make money away from core business, then that will often push the other way.
The default, in my view, is not to spin out unless there's a compelling reason to do so. But from your own point of view, you might want to focus less on the equity question (which is only relevant with one of those paths) than on how you want to be incentivized. That breaks down into how should you be measured, how should you be rewarded based on those measures, and what part of that reward should be short-term cash, and what part in equity or equivalent long-term instruments.