Ideally, you would send your BTC to the mixer and it would forward you on the same amount - fee from a completely separate transaction chain of Bitcoins so that it cant be traced, but in reality, can it work like that unless the mixer has a lot of BTC. If the Mixer has little BTC or is new they might not have funds on another chain to send to you and then they just forward your BTC back to you which has the same trail.
Could someone explain if that is likely the case in this scenario? or are there other technologies at work here?
Don't use any new and unknown Bitcoin mixers because there is high risk of them being a scam, and when you are using legit mixers always double check if you are on real website and not some phishing fake website.
Chipmixer is well know bitcoin mixer that exists for years (since 2017 on bitcointalk forum), they have enough funds for sure and you don't have to pay any additional fees except donations if you are happy with their service.
They are not using any separate chain other than Biotcoin chain, and it makes extremely hard for anyone to track transactions with their chips that have predetermined amounts of bitcoin.
There are other alternative ways for making bitcoin more private with using coinjoins with wasabi wallet or exchanging with other privacy coins but none of them is perfect, and if you don't know what you are doing you can easily make a mistake that negates anything you did with mixing.
2021 List Bitcoin Mixers Bitcoin Tumblers Websites:
https://bitcointalk.org/index.php?topic=2827109