I would check with Siglent EU HQ how much the power supply costs; if it is well under €100, repairing/troubleshooting the old power supply would be of purely academic interest.
If Siglent EU HQ can send the part to the distributors here, then what you suggest could be viable. In Turkey we are limited to a personal import limit of 30 EUR including shipping, so it's either the part can be obtained through the distributor or someone coming from abroad will bring the part. Otherwise it's repair time.
[Just a few notes about the situation here: Above 30 EUR it becomes a commercial item and you are required to file it with the ministry. You as a person can't do it so you must use the services of brokers. What hurdles can the customs throw at you when it is a commercial item is anyone's guess. They could for example ask to have it "certified" by the national standards which could mean you could choose to buy another scope instead of trying to import that part.
Even if the item value is below 30 EUR, the customs may consider it commercial and give you a headache. For example, you order 5 small PCBs from a PCB house in China for $10 and pay $5 shipping. You think all is well because the total value is below 30 EUR but here's the kick: the customs will declare the item as commercial since there are 5 pieces. So instead of paying the fixed 60% tax and having your PCBs, you will be given a runaround and an exorbitant bill to pay at the end.
If you don't pay, item will be considered abandoned and will be auctioned off to be sold to the "merchants" whose business is selling such auctioned items. So, the item that once needed to be "certified" can easily be sold within the country after it goes through the "official" channels. It's entirely possible that you can find your confiscated/abandoned item and purchase it if you somehow can come across it via i.e. a google search.]