Well unless the video sound quality is different to the actal sound you are hearing, to me anyway it sounds like it is the same sound but just a different pitch?
If as you state it is after the bike has been running then it points to the issue being something that changes it's 'state' when warm?
It's likely to be the fuel pump as it primes when the ignition is turned on. This is quiite a relatively expensive piece of kit to replace just because it sounds different when hot. They are (in the UK) about £30 - £40 when sold used but you never know if the one you are buying is in as good condition as the one you have on your bike.
Personally, as you say the bike runs fine I would not worry about it as clearly there is no fault otherwise a fuel pump issue WOULD be noticeable when riding.
Unfortunately there is no way of testing these for people like us and if you did have it professionally tested it would likely cost more than a replacement one.