I edited the recorded file to show what happens when turned on, after 2, 9 and 13 minutes and when the fan is blocked. I annotated the waveform plot so you can see the events and the increasing noise. Hoefully the recording attaches to this post.
Well, this doesn't sound abnormal to me, especially considering that the mic is close to the fan.
I think it might just be your first more modern unit with a fan - I felt the same annoyance when I got my first equipment with fan, introducing a lot of noise to the previously very quiet lab. And the smaller units are even worse - have you ever heard e.g. a Keithley 2001 DMM? That really has some whining tone to it...
Then there is the change of the tone on your unit. I remember that there have been complaints about fan noise in the past and this has subsequently been discussed in Siglent R&D. Back then I mentioned that a temperature controlled fan doesn't add significant cost and maybe this is what has been implemented by now (since Tautech mentions that recent SDS1202X-E are less noisy than the previous units).
The problem is, you will not find anything less noisy out of the box, except a faceless USB-scope, and the same problem will arise with pretty much any modern gear you're going to add to your lab, be it a signal/function generator, spectrum analyzer or even a DMM. Ironically, there are quite a few power supplies without fan, either with a big heatsink for the linear ones or SMPS designs with low power dissipation in the first place.
Anyway, fan noise is an ongoing topic here, for pretty much all devices. Fanless designs are really rare nowadays - and certainly not found in the class of an SDS1202X-E DSO. Users are sometimes "tuning" their gear, fitting less noisy fans, adding temp controllers and/or mechanic decoupling from the chassis.