As others have mentioned, getting a firm price offer from Carmax gives a good idea of what your existing vehicle is worth as a trade in, give or take somewhat.
Last time I bought a car I first got a firm price in writing from Carmax after having already decided on what new car I intended to buy. I made clear to the dealer salesman that I was there only to negotiate the price of the new car, no trade in factored into that price.
After the purchase was a done deal I was asked again if I would sell my current car. I made the salesman make an offer which came up far below Carmax’s written offer. My response was either match the firm offer I already had or no deal on selling the dealer my old car. The dealer matched the offer.
Bottom line, my total out of pocket including sales tax for the new car ended up nicely less by some percentage points and several thousand dollars than the going rate in the area at the time. And I did not have to deal with the hassles and safety issues of my attempting a private sale.
Current market dynamics are such that no matter how you handle buying a car, it is impossible to get a bargain deal on either a new or used car. A current car kept maintained and repaired for now is, in most cases, one’s best bet IMHO.