The other issue is what type of shower nozzle you have? Low flow ones
provide less water but longer showers.

I would install a tempering valve, set the tank HOT thje tempering
valve at the temp you prefer.

cold winter water temp is likely the source of the problem

how many BTUs is the new tank? 75,000 is prefered, many are 35,000
BTUs or less

the tempering valve effectively gives you more hot water and will fix
your problem