I would be looking at a steel framed touring bike with handbuilt 36-spoke wheels. For example Surly Long Haul Trucker (sadly, not available anymore but you can buy the Disc Trucker even today) is rated for 136kg rider and 25kg cargo for 161kg total carried weight. That's in the right territory even though you still exceed it by a bit.
Most bikes come with wheels so you'll at least want to hand the existing wheels to a professional wheelbuilder to touch them up, ensuring they are fully stress relieved, and have even and high spoke tension. Even then, I would be very careful when riding the bike, using high volume low pressure tires (the thickest you can fit) and riding over curbs very carefully. If the spoke nipples tend to loosen and making them evenly and highly tight won't prevent nipples from loosening, you may have to resort to using threadlock on the spoke-to-nipple interface threads. Note that threadlock is still not a substitute for quality-built wheels and often suggesting applying threadlock needlessly is a sign of a poor wheelbuilder, but even quality professional wheelbuilders may have to resort to threadlock in some speciality applications like really high system weight.
I'm bit below 110kg. I know that a rather weak framed Cannondale Synapse Neo EQ e-bike that weighs over 20kg and can carry 16kg cargo withstands my weight. That's about 146kg system weight. In your case, the system weight for a standard non-e-bike would be about 225kg, even more if you carry cargo.
I use 28mm high pressure tires pumped up to 7 bar even at 146kg system weight. If you select for example 40mm tires pumped up to 5 bar, such as Schwalbe G-One speed that are rated for 100kg, you should be reasonably safe. You still exceed the tire load rating because most of the load is on the rear wheel so the rear wheel will be carrying perhaps about 140kg load. But if you ride carefully, that should not be an obstacle. Remember to pump the wheels up every single week, because bicycle tires leak pressure quickly and ordinary riders may have to inflate only every other week but in your case the margin between acceptable pressure and maximum pressure the tire supports is practically nonexisting.
Most likely even though you are heavier than ordinary, your arms probably aren't much stronger than ordinary, so most of the weight is carried not on the handlebars/stem but rather on the seatpost. Thus, select a two bolt seatpost where the failure of a single bolt won't make the seat loose. Ideally the seatpost would have polished smooth, not anodized surface, because polished components have higher fatigue endurance. I would also not ride without mudguards and rear rack -- if your seatpost fails, your butt will hurt a lot from the spinning rear wheel onto which it falls. The mudguards and rear rack cover the spinning rear wheel. Also I suspect you need a really big honking seat collar because your seatpost WILL slip. Surly Constrictor is one that's compatible with Surly Long Haul Trucker and I suspect Disc Trucker too.
Inspect your high load components often for beginning cracks. That includes in your case very dense inspection schedules for at least seatpost, cranks and fork. You might to want to keep an eye on the handlebar and stem too, although I suspect they won't receive much of the extraordinarily high load. The fork should be pulled regularly and have its steerer tube inspected for fatigue cracks. Similarly don't just eye externally the seatpost, rather pull it from the seat tube, regrease and reinstall. Might be good to check the welds of the frame often too. Usually, for riders with ordinary weight, frame failure won't cause the rider to get hurt, but in the case of very heavy riders, it's possible if one weld fails the remaining welds can't withstand the high weight and fail too immediately at the same time.
You'll wear out the wearable parts -- chains, cassettes and brake pads -- very fast. Keep a stock of spares. Also bottom bracket is something that can fail at any time from the high weight so keep one at spare, and if you don't want to stop riding waiting for a replacement seatpost or crankset to arrive one of each in spares should prevent that wait. Hub bearings might wear faster than ordinary from the high weight too. I suspect that cup and cone bearings, being full complement, last more than standard industrial machine bearings that are half complement.
Then there's the braking problem. Normal weight riders can usually brake so hard using only the front brake that the rear wheel rises into the air. You probably have to use both brakes at the same time, because otherwise you won't get enough braking force. The low mechanical advantage and flex in bicycle brakes otherwise would prevent an acceptable braking force.
