Should the wheels be trued? (There is no obvious run-out or lose spokes.)
A high quality wheel that is true to begin with will stay true. Unless there's an obvious issue, don't true the wheels.
Wheel truing is sometimes advertised by bike shops as something that is done at the first service. However, it's highly binary: most bikes have lightweight riders who never cause any wheel spoking issues, whereas a small percentage of bikes have heavyweight riders who can cause the wheel to completely and totally lose all spoke tension. So for most bikes in the first service, no truing will be done.
A wheel that has withstood the test of time for 25000 km is an excellent wheel. Early-life issues like spokes breaking have been eliminated as a possibility, and you can be far more certain the wheel stays working than for something that has 0 km and no test of time behind it.
Do the wheel bearings and bottom bracket need maintenance?
Bottom brackets don't require any maintenance today. It used to be the case that bottom brackets were possible to be disassembled, but long ago even square taper bottom brackets switched to cartridge-style units (which you don't repair but replace) and today in Hollowtech II cartridges are all we have ever had.
Some higher quality wheel bearings like Shimano are adjustable and repairable. If you have ridden 25000 km, it might be a good idea to disassemble the hubs and put new grease in and re-adjust the bearing play. You need cone wrenches with sizes suitable to your hubs to do this service. Fortunately, cone wrenches are cheap.
Some lower quality wheel bearings from manufacturers that do not have cup and cone manufacturing capacity use standard machine bearings in wheels. They are usually half complement, so they have only half the amount of balls a high quality cup and cone repairable/adjustable bearing would have. They probably fail earlier than cup and cone bearings, and should they fail, the only thing that can be done to them is swapping the bearing units with a bearing press. Most cyclists do not have a bearing press at home, so this is a bike shop job.
You briefly mentioned issues in two important bearings.
Headsets today use 45 degree cartridge bearing units. In this case, the bearing is actually a compound bearing: the 45 degree interface absorbs vibrations that would cause the main bearing otherwise to fail in an "indexed steering" mode. These headsets should be disassembled occasionally, once per 25000 km is fine, and you should add grease on all 45 degree interfaces and re-adjust the bearings. If you fail to keep it greased, it can fail in the "indexed steering" mode, developing notches that prefer to keep the fork straight.
Pedals have bearings too. Lower end pedals might not make sense to overhaul (you replace the entire pedals instead), but if you have expensive pedals, it may be worth the effort. Companies like Shimano that have lots of manufacturing capability tend to use cup and cone bearings that are adjustable and repairable, so you might want to occasionally overhaul your pedals, but companies that lack the manufacturing capability cheap out and use standard half complement machine bearings. The machine bearings probably fail earlier and should you need to swap them, you'll probably need a bearing press.
Do I need to replace the brake rotors if they still look and work fine?
Measure the width of the rotor from an area that touches the brake pads with a micrometer screw. Due to wear they are concave so caliper is less ideal than micrometer screw. Shimano says that 1.5mm thickness, Shimano brake discs should be replaced. Other manufacturers probably have similar wear limits, and the wear limit may be written on the disc itself.
Do I need to replace the cassette/chainrings? (They are noticeably worn but the chain still runs and shifts very smoothly.)
You only replace these if you have issues.
I'm surprised you have managed to get 25000 km from a single cassette. Usually I'd say that 10000 km - 15000 km (after about three chains), the cassette should probably be replaced. If yours is still working fine and the chain doesn't jump on cassette teeth when pedaling forcefully in the smallest sprockets (hardest gears), then don't replace. The moment to replace usually happens when an old chain worked perfectly with the cassette but a new chain refused to work without jumping on the teeth. I suspect the next time you replace your chain, it's time to replace the cassette too so make sure you have one unused cassette in stock, as bike parts are hard to obtain these days. Also you should keep one or two unused chains in stock as well.
Chainrings are a different matter. A high quality chainring can last as much as a typical car engine, hundreds of thousands of kilometers. The teeth can show visible wear yet the chainrings still probably works. You only replace chainrings when you have issues such as chainsuck (chain failing to disengage from chainring). You might want to occasionally rotate the chainring on the crank, so that wear happens at different portions than previously. On 4-pin chainrings, you rotate by 90 degress; on 5-pin chainrings, you rotate by 72 degrees. However, if the chainring has shifting aids they may be at different points if rotating so shifting could suffer but you get more miles out of the chainring.
What other things might I be overlooking that should not wait until they become a problem?
Check that bolts are torqued and stay torqued. Even something as mundane as front fender bolt can be a major hazard as the fender can become loose and jam in the fork, flying you over the bars. If some bolt doesn't stay torqued, put threadlock like Loctite in it. However, don't continuously re-torque the crank bolts if you have square taper cranks. The problem is that they are torqued to 40 Nm, then the crank squirms on the taper and they lose torque. If you continuously re-torque again and again to 40 Nm, the crank squirms on the taper a lot causing potential damage. Crank bolts are items that are torqued only once to their correct torque and then subsequently you can check lightly if it still has some torque on it, but never retorque again to 40 Nm.
Inspect every high load area often for signs of beginning cracks. This includes seatpost, fork, stem, handlebar and cranks. I wouldn't replace any of these components on a schedule. If you are observant when you ride and notice any oddness in handling, and if you inspect these often, you can probably catch a starting crack before it causes the part to separate in half. Clean the part before inspection and use a flashlight aimed from different directions to see if you can find any cracks.
Replace rear derailleur jockey wheels as they wear.
Check your emergency repair kit occasionally. The checks should include:
- Whether the mini pump still works
- Whether the spare tube still holds air (a good idea is to insert the spare tube in a sock that prevents the rubber from wearing fast)
- Whether the vibration of the toolkit has caused unused tube patches to lift on their edges
- Whether the tube patch glue has dried out
You already mentioned several important things but I'll repeat:
- Brake pads
- Bar tapes
- Brake lever hoods