Answer: Its all about risk (for you) and liability (for the maker/seller)
A bike rated at for a X kilos will not suddenly fail at X+1 kilos. However beyond this point, the likelihood of load spikes increases, so the whole bike suffers and deteriorates faster even if you only ever ride in steady state. This might be known as the "knee/elbow" of a graph.
Naturally manufacturers/importers want to minimise failures where they have extra costs, so a weight limit helps them. This is similar to saying "this bicycle is not for stunt riding".
The risk to you is, what happens if a part fails catastrophically while you're riding? If you're going slow vs a medium or even a high speed failure?
A simple fall for a heavier person is on average more damaging than the same fall for a lighter person. Add some forward motion, and the momentum can make a minor graze into a more significant cheese-grater, and depending how you land can transform a bruise into a break. These are the risks.
Minimising risk To do so, look for a bike with certain features
- Higher-spoke count wheels. There's a trend to reduce the number of spokes and call it aero and weight saving. But ideally your wheels would have a minimum of 32 spokes on the front and 36 spokes on the rear. If possible, 40 or even 48 spokes on the rear would be even stronger, but will cost/weigh more.
- Metal frame. Anything that can be described as having a "sudden spontaneous failure" should be avoided, so that rules out Carbon Fibre as a frame material for your bike.
This leaves Steel or Aluminium as your primary options, with exotics like Titanium as rare possibilities. Steel would be ideal for your needs because it is relatively elastic, and its failure modes tend to be quite gradual. A steel frame will bend or tear, but generally will not part completely.
Aluminium would be another common possibility, but suffers from "work hardening" so as an AL frame is stressed and relaxed, it will slowly get harder and more brittle. That said, it takes decades to "wear out" any aluminium frame so if you're going new, then this isn't an immediate issue. If you're going second-hand, have a very good look over the whole frame before committing, looking for dents and cracks.
- Diameters - In the old days a 25.4mm (1") seatpost was enough for everyone. Now there are more sizes, and strength goes up as diameter increases. So look for oversized seatpost of 31.6mm, and handlebars of 31.8mm.
- Tyres - you're talking about mostly road, sealed paths, maintained gravel paths, and not-hard trails. Realistically, these are not challenging surfaces for a tyre. Aim for 50-63mm (2"~2.5") tyre widths, and look for smoother tyres without aggressive knobs. A slick tyre would be fine for road usage and would be less effort to ride, while probably being adequate for any pathway.
- Suspension - possibly contentious, but IMO you don't need any suspension on the road at all. It tends to add weight and compromise the bike, and the returns aren't worth it. This also includes suspension seatposts and suspension stems. Same goes for simple paths which are really just roads for feet. The only time suspension might help you is if you're going fast and don't take a good line, ending up somewhere bumpy and going too slow, resulting in a fall.
Upshot - if you can ride the path without your tyres leaving the ground then suspension isn't really needed.
If you DO choose suspension, make sure its rated for your weight, which is not the same as any limits on your frame. For air suspension you'll need an air-shock pump to add air when setting the sag. For coil sprung suspension you'll probably want the bike shop to help set it up for you with the right number/grade of inserts. For this reason, a tuneable air-suspension would be better than a coil-based suspension.
- Pedals - decent quality flat pedals are all you'll need. Avoid clipless/cleats at this point, save that for the next bike. Flat pedals also help you get a foot down quicker should that be needed.
- Saddle - avoid big wide squishy padded saddles - they may look comfortable but they tend to not be. Instead search here for "saddle width" questions.
- Position - Aim for a bike that lets you ride with a more upright-position. I found that my gut was in the way on a road bike to start with.
Another option for you is to look at a tricycle or trike. They have an extra rear wheel and will carry more weight than a two-wheeled bike. Downsides are they're wider, and tend to cost more due to rarity. Overall stability is lower too because they always conform to the slope of the ground, but on flat land its impossible to fall off. They tend to appeal to the elderly who may have balance issues, so resell value is generally okay.
Speaking of resale value, a well-specced "heavy rider" bike should hold its value and in a couple of years can be sold off once you no longer need it.
"Fat bikes" are called that because of the width of their tyres, not because of the rider. So don't assume that having big wide tyres means a bike will work for your starting weight.
You can chart your weight over time - I log my weight first thing in the morning, and additionally after significant exercise which reinforces how much good each ride is doing. I ride mostly to commute, which means I have to ride whether I feel like it or not.
Upshot - yes I would observe the weight limits of manufacturers, but consider it motivation.