It'd fairly simple to make sure you are in the clear. Google the song, find the composer and see if they have been dead more than 70 years - in most, but not all territories this is the decider. So George Gershwin's music is OK, but his brother's words are not. In general. As in if it says words AND music and one is +70 yrs dead, and the other +69 years, you have issues.
If they are less than that 70yrs, then their work is still within copyright, so you move to stage 2 of complication. Youtube, identify music and they get any royalties youtube generate, but they don't take your music down unless the rights holders and their agents have a bee in their bonnet. Some Beatles stuff and other material by people who have strong feelings - simply refuse to allow the work to be used at any cost - so these people get youtube soundcloud and others to remove them completely. Youtube's copyright strike.
Just determine the 'owner' and fire away. Some are lost in time - others absolutely not!
If you follow the chain for Autumn Leaves, you find the original composer was Jospeh Kosma - and he died in 1969 - it's 100% NOT in the public domain, but one of those songs covered and adapted so much that it's treated like it is - but the family of the writer could fight for their rights but they don't seem to - maybe the CD income from big names is enough for them. The few dollars your version might earn on the streaming platforms probably don't worry them, and in fairness, many arrangments are quite distant from his original. ASltered melody, altered chords, different arrangement etc. However - you need a licence in some parts of the world. Here in the UK, you 100% need a licence for CDs, DVDs, records etc - but streaming services in the UK seem separate. Streaming from the UK to the US apparently does need a licence - but getting one yourself is complicated. However - the shysters at Distrokid, who I hate with a passion will happily get you a worldwide licence and distribute your music worldwide, simply - and you get paid too. They have a habit of dumping people when their sales creep up - so take care. I'd suggest them for covers, but not for your own work.