I'm planning to upgrade my rear cogs and Rd with a 9 speed Sora and I want to retain my 3x setup. I already found the r3030 which is 3x9 Sora shifter. My main concern is if the Tourney 3x FD compatible with Sora 3x STI and 9 speed. I'm wondering if there's gonna be a chain rub when I'm on the biggest or smallest cogs. I'm also going to reuse my Shimano FC-TY501 which is 3x with 48t on the biggest.
It doesn't appear as though your changing anything in your front drivetrain which if designed for 8 or even seven speed should play well with a 9 speed rear drive train. You'll need to get a new 9 speed chain for good shifting in the rear. It's also a wise thing to do for a new drivetrain as a worn chain on a new drivetrain accelerates the wear on it if it doesn't skip which will be bothersome straight away.
The mentioning of 105 and the implication it is your current 3x front is confusing. The 105 groupset is a step or two above Sora and is currently 11 speed compatible. I believe the 5700 model number was the last 10 speed 105 group, however you mention having 48t large ring, a compact crankset, and IIR, that began with the first 11s group model number 5800. The issue is if the 105 front drive is 11s, the wider 9speed chain you run on it may make more noise than is expected (or can be tolerated). You could use a 10 speed chain to split the difference in the 11s front/9s rear, which will function just fine on both.
There is always a risk of chain rub on the front derailleur cage when the chain is on the extreme ends of the cassette. Shimano road front drive shifters have extra detents/clicks that are "trim" positions. It's like a partial shift in that the cable and derailleur move but not so much that it moves the chain to another chainring. This allows the derailleur cage to get out of the way of the chain, preventing rub, but not changing gears. A solid set up of the front derailleur can prevent a lot of chain rub and then the trim feature can eliminate it all together MOST of the time.
Generally, my point is that one can mix front and rear drivetrains from different speed classes. These set-ups work best if there is only a +/-1 speed difference, and the chain is specific to the rear drive. The rear shifter needs to be the same speed as the cassette for a few reasons, however the front is fairly flexible using the +/-1 rule for both chain set and front derailleur. Any 7,8,9 or 10 speed Shimano road rear derailleur will work within any of those speed classes as long as its within specs as far as appropriate cage length and total capacity capability.