You can use almost any MCU with an ADC - you'd have to be trying quite hard to not meet +/-5% without calibration! Don't let the tail wag the dog - choose the micro based on more important factors such as familiarity, development tools, support, availability etc.
The internal references are often rather poor so if it isn't accurate enough then amost all (all?) MCU's allow you to use Vdd as the reference - either through an analog supply voltage pin Vdda (or the like) or directly from Vdd (Vdda may be internally connected to Vdd on small packages). Many low cost regulators are available with output tolerances of +/-2% including initial tolerance and full temperature range. Eg. the AP2022 cost < 7 cents:
https://www.avnet.com/shop/us/products/diodes-inc/ap2202r-33tre1-3074457345631341369?CMP=EMA_Octopart_inventoryfeed_VSE?aka_re=1Additional error will come from output load current regulation, amongst others, but that may well not be much of an issue as the load current will be often be pretty constant when you are taking measurements with the ADC. Noise may be an issue but lots of averaging may suffice.
If that isn't good enough the AS431 (or AP431S) is a 2.5V .5% reference with maximum .4% deviation over -40 to +85C. It costs < 4 cents:
https://www.avnet.com/shop/us/products/diodes-inc/as431antr-g1-3074457345625002707?CMP=EMA_Octopart_inventoryfeed_VSE There are many other TL431 variants but this has the best temperature spec as far as I can see and is also the cheapest.
If you don't want to spare an ADC input to measure the reference you could use it to supply the micro directly (<100mA) or buffered using a transistor or even a voltage regulator. This has the extra benefit of saving the cost of the regulator. Be aware though that TL431 references can be a bit tricky wrt stability so some care would be required.
All solutions will have long term drift to contend with but this is often poorly, or not specified for low cost devices. I don't think I've ever seen a drift spec greater than 120ppm per sqrt(1000) hours for references which equates to .08% over 5 years so probably not a big concern. When specified it is usually at 25C so a regulator running rather hotter would likely be worse so some Arrenhius calculations might be in order.
Your 1% offset allowance is very high - I expect most MCU ADCs have specs of 2 or 3 LSBs offset at most so < .3% for a 10 bit device and probably rather less than .1% for most.
I'd be careful about your 1% allowance for voltage divider error; if the divider ratio is 1:9 or less the error approaches twice the tolerance of each resistor. So a 1% error would require each resistors to remain within .5% of nominal over life which is a challange unless you are buying relatively expensive parts. Eg. Yaego RT series .1% thin film are around 4 cents, but look at the specs for the various drift factors: .5% max for soldering, another .5% for 1000hrs load life at 70C, add .5% max for humidity exposure, plus .5% for low temperature exposure, vibration, board flexing etc. etc.
And then there's the shelf life stability, assuming the resistors spend most of their life at benign temperatures - but that is rarely specified for lower cost parts. You could easily get to 2% or more over the life of the equipment depending on which factors you choose to include. In reality you are extremely unlikely to suffer such drift but 1% is easily possible.
Vishay Beyschlag 25ppm .1% MMA0204 cost around 15 cents from Digikey but have much better stability specs so .5% total drift over life should be easily achievable.