As a friendly heads up to anyone exploring this space — temperature control is a complex dynamic between many components, chiefly the mixing valve, any local thermostatic dampers in the valve (rarer, but definitely a feature of high end mixers), and the source of hot water itself . Mixer taps are not simply mixing hot water at temperature H and cold water at temperature C. The temperature H which your hot water sourc…
So we need like a capacitor for hot water at the shower head.
For 2.5 GPM (typical shower) it can do 35°F heating. If you have a low flow shower head (1.75 GPM), you can do about a 55 °F heating.
You could also do a water heater booster - https://www.rheem.com/innovations/innovation_residential/wat...
Another approach is to go to the other end where you've got the tank running higher than is safe to safely touch (e.g. scalding) put put thermostatic valves on all sinks and showers. This way you can run the water heater at 140° then then use more cold water to reduce it to the proper temperature which is a slightly easier problem than running your water heater at 120° and then cooling it down to 105° which gets to "mostly hot water with cold water for pressure". Running a tank at 140° also inhibits bacterial growth (e.g. legionella)
Not enough for a shower, but for a sink you could look at an under sink water heater ( https://www.homedepot.com/p/Bosch-2-5-Gal-Electric-Point-of-... ) - but you're looking at 6.8 GPH recovery time rather than a 2.5 GPM flow rate. The main advantage there is that you don't have move the hot water from the water heater in the basement all the way to a sink (lots of hot water in the pipe that then gets wasted) and thus less water use to get hot water to the sink and less hot water use overall.
An under the sink tankless looks like https://www.homedepot.com/p/Rheem-Performance-6-kW-1-0-GPM-P... with 0.5 GPM for a 65°F raise (you wouldn't even need to run hot water to that sink - this is what I do for my upstairs bathroom since the water heater is so far away that you need to run the water for a very long time to get the sink up to 'wash with hot water' levels).