You're basically thinking of a tank near/above the boiler that pre-warms the cold feed from waste heat (the warmth of the boiler room) - If installation cost was no object, hand-wavingly it will help. So if you can do it at a fairly low cost, it should save a bit.
Getting to hard numbers is fairly difficult, or very easy if you knew some unknowable things.
A gallon of #2 fuel oil is roughly 138,000 BTUs - if we give your boiler the benefit of the doubt and say it's 85% efficient (a few might be more, a fair number will be 80 ) that means you'll get 117,000 BTUs from each gallon burned.
1 BTU heats one pound of water one degree Farenheit. 117,000 will heat 1800 lb of water from a "cold but not frozen" 34F to "might be a warm shower" 99F - that's roughly 225 gallons. If you prefer a "very hot" 120F shower, 170 gallons.
That's the easy part. The hard part (or mass of made-up fudge-factors) is "and what will the tempering tank do for the input water temperature" - to the extent that it directly sucks heat, it will make no difference (you're still burning fuel to heat your house and water, you're just shifting it around a bit) but to the extent that it "scavenges" heat that would otherwise be wasted, there is a savings. If the input water temperature was raised 21 degrees to 55, you'd get 225 gallons of very hot shower from your gallon of oil. If we make the ballpark assumption that you use 17 gallons per shower, you'd get 3 "free" showers (13 for the price of 10) Which is 25% savings looked at one direction, 30 the other. But "garbage in, garbage out" rules here - while I'm trying to speculate reasonably, it's just speculating. what the actual effect on your water heating will be is essentially unknown until you try it, though you can possibly make more educated guesses by considering things like the average temperature in the place you'd be putting the tank, your actual shower times and shower flow-rate, actual water temperatures in and as you shower, etc...
If you can fit the appropriate drain pipe below your shower, there is a neat widget that plumbs the cold-water to the shower around a copper drain pipe from the shower, pre-warming the cold water to the shower as you shower, so you can use less hot for the same shower temperature.
We have a circulation pump that was in the house when we bought it. The instant hot water is nice, but it is a huge energy waster, as you suggested. Our solution was to put switches on the circulation pump. It's plugged into a receptacle near the water heater, so it was as easy as making that a switched receptacle. We have switches (timer type that turn themselves off soon after you turn them on) next to the shower and by the kitchen sink. It only takes about 30 seconds for the circulation pump to get the hot water to you, so we just turn it on while getting ready for the shower (or while stacking the dishes). So convenient, but without the wasted energy or water.
Best Answer
There are three subjects to consider here.
Is your water heater working correctly. It is possible your water heater needs some maintenance as there could be too much buildup on the inside or a heating element that needs replacing. https://www.hometips.com/repair-fix/hot-water-heater-problems.html
Second the water in a water heater is usually hotter than you can use it. Then you add cold water to bring the temperature down to a usable temperature. That way a 40 gallon tank at 130 degrees should be able to produce a lot more than 40 gallons of 100 degree water. You can always turn up the temperature of the water heater. Most electric tank heaters will reach 150 or more degrees.
The last possibility is upgrading. For 400 dollars US you should be able to have a small tankless point of use water heater professionally installed for just the tub. They cost less than 200 dollars for just the unit if you know how to install one.
A full sized tankless water heater will cost you at least a thousand to install. If you get a gas tankless water heater either install in directly on an exterior wall, or get one that uses PVC venting. Metal vents that cheap systems use are wildly expensive.
And a larger tank water heater will cost whatever you want to spend on it plus a few hundred to professionally install. I'm seeing example prices between 500 and 1500 dollars US for a 50 gallon or larger tank depending on the efficiency. Gas water heaters have a much faster recovery rate than electric. It is possible that as 40 gallon gas water heater is all you need.