I think without humans all the ecosystems would recover, but won't necessarily be the same as before and how long it takes would vary wildly from place to place and depending on the extent of the damage. There will be species that go extinct, both because humans pushed the population to critical levels but they never recovered, and because the post-human ecosystems adapt in a way that doesn't enable certain species to survive any more.
Look at how the Earth recovered from previous mass extinction events. Ones that wiped nearly all life on Earth, where only a few things survived, but those things evolved into new species, including completely new megafauna. Life finds a way and as destructive as humans are, we aren't close to wiping out every last bit of life on the planet. Whatever's left will evolve to adapt to the way the planet is. It's helpful to think of ecosystems rather than individual species. Where species are lost, they will eventually be replaced by whatever evolves to fill those ecological niches. Past mass extinction events give us clues as to how long this would take, but the extent of the disruption is a factor. Humans not being there anymore isn't the same as a volcanic winter.
There will always be traces of humans, such that any alien species or newly evolved sapient species would be able to find traces of humans, including traces of shipwrecks. The question is what level of technology they would need to discover them. For example, Victorian scientists discovered Neandertal bones - you won't find them without digging. Modern scientists discovered Denisovans by analysing the human genome and sequencing the genome of a toe bone fragment in a cave in Siberia, and have discovered traces of Neandertal DNA in caves where no other Neandertal remains have been found. You need much more advanced technology than digging implements to discover this kind of thing. So it all depends on who's looking and if they are actively looking or just seeing what's there on the surface.
Also, there are still the remains of shipwrecks that are much older than the Titanic. The Mary Rose is the most famous British one. It was Henry VIII's ship which sank in the English Channel and it survived for centuries and was dredged up in the early 80s (I remember watching it being recovered on TV when I was in primary school) and is on display in Portsmouth (which is on the south coast of England) if you want to go and see it.
I've watched documentaries about even older shipwrecks - from ancient Roman/Greek times. The building materials were different to the titanic - mainly timber. Not only have the shipwrecks themselves survived but often some artefacts from trading ships survive also. One documentary, the ancient shipwreck site had lots of amphoras, which they could forensically analyse and find that they contained some kind of oil. (I forgot the exact details.) Even if iron/steel hulls may rust away given enough years, there will be other materials that don't decay so fast. Even the timbers of antiquity haven't all rotted away. There will be non-perishable materials left behind such as cargo.
There are various documentaries about old shipwrecks, what's left, how scientists have analysed them, etc - I don't know what streaming services outside the UK would have them, but on Disney Plus in the UK there's the National Geographic sub channel, there's the Drain the Oceans series which is about archaeology under the sea - I'm pretty sure the above examples that I remember (i.e. the non-Mary Rose ones) come from this series, but I'm not 100% sure because I watch a lot of these kinds of documentaries. It's fascinating and will probably help you find the answers to your questions about what evidence, if anything, your story's characters would be able to find of shipwrecks. If you look up about the Mary Rose you can find all kinds of info online, not just on the ship but also extensive archaeological studies done on the human remains and other artefacts found within the wreck.