The claim you refer about Apple purposely making the phone slow is one of these things that can seem both true and false depending on your point of view.
The short version of that story is that the battery in your phone is a wearpart - and as it wears down it will loose capacity and perform worser. At a certain point the battery is weakened so much that you risk the phone just spontaneously turning off as the battery cannot supply the necessary power. At that point Apple applies "performance management", which essentially means making the CPU a bit slower in order to consume less power and prevent the phone from turning off unexpectedly.
You can disable this behavior from Settings > Battery > Battery Health. It will display the following text if performance management is applied:
"This iPhone has experienced an unexpected shutdown because the
battery was unable to deliver the necessary peak power. Performance
management has been applied to help prevent this from happening again.
You can disable performance management to ensure the CPU is run at full speed again. However, it will automatically be turned on again, if the phone is unexpectedly powered off due to battery problems.
Essentially if your current battery is worn down, you want to replace the battery to fix this problem.
However, if your previous battey was worn down and performance management applied - and you replaced the battery without disabling performance management again, then you can simply disable it to regain performance. If you used an official, authorized repair shop, they should have done this for you as part of the battery replacement though.
All in all the "truthiness" of the claim now depends on whether you think an slightly throttled iPhone is faster than a non-throttled iPhone that might turn off at the most unfortunate time.