Your old Sony DVD player will definitely still work, it's just a matter of getting the right adapter. If it uses those yellow/red/white composite cables like most older players, you can grab a composite-to-HDMI converter for like $15-30 online. Plug the DVD player into the converter, then run HDMI from the converter to your TV, and you're set. Component cables (the red/green/blue ones) also work the same way with a similar converter.
The thing everyone seems to skip over though: make sure your converter actually has the right power adapter and supports your specific cable type. Some cheaper converters are finicky about older equipment, and you don't want to buy one only to find it doesn't recognize your player's signal. Also, even with a converter, the image quality won't be stunning on a modern 4K TV since DVD is just 480p, but it'll work fine if you're just rewatching stuff you like.
Honestly, if you've got a stack of DVDs you want to rewatch, it's worth the adapter cost. Streaming is convenient, but there's something nice about having physical media that doesn't depend on your internet or a subscription staying active. Just test it with one converter before committing to a bunch of them.