Sudden loss in water pressure, but in weird places

Old water heater which was never inspected started leaking from the bottom and was replaced

New water heater appears to provide much lower hot water pressure nearly everywhere. Not only that, probably when no one else was using anything, I have one observed the water pressure suddenly jump up while I was using it on the first floor. It could have been the washer in the basement stopping, but anyway.

The thing is that the hot water pressure in the sink right next to the water heater in the basement seems to have gone up vs before.

The most common solutions proposed are blockages, however it's highly unlikely that the day after a 100% new and modern water heater was installed that pipes got blocked.

Unclear how to resolve the issue.
Some more information: In the 1st floor, there's a kitchen sink head which used to have a function that sprayed the water, but required a certain amount of constant pressure to maintain that setting. Now, it will never work because of low pressure. We unscrewed the head and the hot water pressure seemed to be very significant. I don't know if that's normal or not.

verify the dip tube is inserted into the cold side of the water heater

The psi on the cold side is what pushes your hot water through the water heater. You may have a block in the 3/4" that comes off the water heater or like frodo said the dip tube isn't in. Check the cold water valve above the water heater maybe it wasn't fully opened back up

When you replaced the heater, it’s likely that sediment and rust got loosened up in the pipes.

Now some faucets and fixtures are clogged from that.

The kitchen sink faucet has at least three places that can clog up, the aerator, the flow restrictor, and the check valve.

Look at videos on Youtube about how to locate and clean or replace the little parts in these clogged areas.

Google searches will lead you right there.

Same for slow bathroom faucets, shower heads, slow toilet refills.

Your problem is not low pressure, it is low flow, caused by restrictions.

Based on your description of the situation.

Yes, pressure and flow will rise or fall as other big fixtures open and close their valves, I think everyone knows that, just common sense, think about it.

Thanks. Issue resolved, it was something which got released or loosened after the heater was replaced. Didn't expect that.