Canning tomato sauce for the refrigerator

As you state, you have not followed any canning procedures, so you don't get any more storage time than the standard recommendation. Glass vs plastic doesn't matter. So, I would just recommend freezing. Tomatoes, and tomato based sauces for that matter, freeze nicely. If you use freezer, zip-style bags, you can freeze them flat. They will then thaw rather quickly.

Anyone here who gives you an estimate beyond what a typical (non-canned) refrigerated sauce would last is just going to be speculating.

The thing about canning recipes from reputable sources is that they are tested scientifically. They often run hundreds of trials with testers for a particular recipe, then test each for bacterial growth, etc., before deciding a recipe is safe.

And the somewhat unfortunate thing (for your purpose) is that most of that testing has been done with the goal of having an unrefrigerated shelf-stable product. There are a lot fewer recipes and processes that have been tested that way for products that will be sealed and refrigerated afterward.

That said, the growth of the market in refrigerated convenience foods in recent years has led to new commercial processes. At a grocery store, you can sometimes find things like refrigerated soups or sauces that are sealed and have a somewhat extended lifespan (from a couple weeks to a few months). They won't last as long as a room-temperature canned product, but there are additional processing steps taken to give them a longer shelf life. (Some of it is due to preservatives too, but there are often processing steps similar to canning to add to shelf life.)

To my knowledge, most of these processes are still primarily handled on an individual basis by commercial producers, who often have to do testing themselves to ensure their products will be safe. I don't know of any reputable resource that discusses home recipes for sealed jars under refrigeration and their shelf-life. (The other aspect to the traditional canning recipes is that they are usually structured to keep stuff safe indefinitely under storage, rather than targeting a specific shelf life.)

So, in your case with an untested recipe and untested process, it's all just speculation. The biggest factors in spoiling of tomato sauces in the fridge are often due to mold and other spores that get into jars, so it's probable that your technique will stave off that concern a bit longer. But as to precisely how long your sauce will be safe, no one here can tell. Without testing, there's no guarantee it will have a safe shelf life beyond that of any unsealed refrigerated sauce you put in Tupperware or whatever other container.

Athanasius is correct that any comment you'll get here is anecdotal at best - so here's my anecdote. We do exactly this regularly (we make a batch of Marinara, put it in a mason/bell jar with a standard canning lid directly from the stove, let cool, then put in the refrigerator or freezer).

We don't get much more than a week, maybe 2 at most, before mold starts visibly growing in the sauce typically. We certainly don't plan for more than 7 days in the fridge. Nearly all of our sauce, except any we immediately plan to use and/or any small leftovers from a usage that are not worth freezing, is put in the freezer as a result. I recommend the same.