I will be located in a country where the Internet is EXTREMELY controlled and filtered. Not sure if I can even bring my current router with me(seems forbidden), so turning my RPi4 seems a good idea... Don't you think?
You'll need a USB 3.0 to gigabit ethernet adapter and a separate gigabit ethernet switch, but this setup is considered to be excellent as a lower-cost OpenWRT solution.
Alternatively you can use a managed switch and use vlan tagging, but this is slightly more complex and effectively makes the link half-duplex (up and down have to share the gigabit link, e.g. with a 100 mbit/s upload running you will be capped at 900 mbit/s download)
Depends on if you're allowed to bring the Pi in at all. Might be safer to just buy what you need "on site". There's a lot more to this than just the technical side.
Whatever you do, just be careful. A lot of places don't play easy with foreigners breaking the law. It can be easy to hide what you're specifically doing over a network, but they don't need to know what you're spefically doing to say "bypassing the filter at all is illegal", "using tor gives us probable cause".
Depending on your situation and how they check things you bring in, it might be better to just load up a/some big hard drive(s) with enough content to carry you through until your next trip outside the filter. Knew someone who was in a similar situation for a long while that would emulate their way through old console game libraries like that.
May be worth looking into how political dissidents can protect themselves. Hidden encrypted containers. Private vps outside the filter that you connect to, doing all your questionable shit on the remote server outside, so the only data transfer is video feed to/from. If hiding what you're doing is needed, steal notes from the people with lives at stake.
So much of this depends on specifics it may not be safe for you to share. Probably worth asking questions in some of the privacy focused communities.
OpenWRT won't hide what you're doing from the network that handles your internet connection. It's just an option for something you could use as a router/wifi AP.
I don't think it's usual to forbid bringing hardware. And in some (many?) internet-restricted countries VPNs and things are also not illegal of themselves, and still less punishable normally. Because practical reality is foreigners have a variety of reasons for circumventing restricted internet and the state's interest is mostly in restricting their own citizens.
Silly question but why are you going there? Maybe this a chicken and egg problem. You are trying to have freedom in a country set on restricting freedom. Maybe rethink and redefine your adversary. Ask yourself, am I breaking local laws? If so, how can I hide and what are the consequences of being found?
The last thing you probably need is to be arrested.