Home waterline upsizing questions
The time delay between the hot water tank and the places where you use it is entirely determined by the distance between the two, which you have not changed. Note that larger tubing would be counterproductive here, because the flow is almost entirely determined by the outlet device, and you want to minimize the amount of cold water you need to drain before you start getting hot water.

Similarly, the pressure drop issues when using more than one tap are also related to your inside plumbing. What this tells you is that the badly corroded service pipe was not your "bottleneck".

The only way to improve the hot water access time is to move the tank closer to the places that need it. In a large house, this may require multiple heaters, possibly including on-demand "tankless" type heaters.

The only way to improve the pressure drop issues is to redo the interior plumbing, either by using larger tubing, or making every tap a separate run from the main distribution point. With modern PEX tubing, the latter option is less trouble than you might think.