I say it depends on the old hardware and your expectations.
For example, if you just want to build a new server for the heck of it, then do it. As a nerd you will of course do the reasearch into the hardware you need for your list of requirements. I will not presume that TrueNAS will be your server choice but if it is, there are some requirements.
Do you want a very energy efficient server? How fast should it be? And a big one, how much are you wanting to spend? How much storage is generally an easy thing if this is just a simple storage server. If your needs are modest, you can have a decent system and highly reliable system with TrueNAS.
But! TrueNAS is not a set and forget system. While many people do that, years later when a drive fails, they panic because they don’t remember how to read a user guide. Pity.
I have a little script that helps to make keeping you engaged a bit easier and I’m not pushing this scriot on anyone, but it does help those of us who do not want to babysit a server. Of course that is for TrueNAS.
If the setup you have now is fine for you, maybe replacing a HDD with SSD is something you would entertain. A little less power use than a HDD. If you do keep the old system, i recommended you replace all the fans, including the one in the power supply if you are able. Blow the dust oit of it. Give it a good checkup by running Memtest86 and a CPU stress test like Prime95.
I built an all NVMe system last December and love it. Well except the case I’m using was a terrible choice for air flow. But it is a tool less case so it has some advantages.
My advice, think about what you want and what you need. Choose the path you want to go down.
We here will provide advice on hardware to some extent and remember, you get what you pay for. Don’t but cheap stuff without your research.
Best of luck to you and welcome to the forums.