Method for including bacon in an otherwise vegan chili?

You have two different approaches from Catija and eckes, depending on what you favor, but you could also combine both approaches -

Start by chopping up the bacon, and then cooking it in the pot until it's nicely crisped and the fat is rendered.

Remove the bacon with a slotted spoon, to paper towels to soak the remaining fat from the bacon and leave it in it's crisped state. Leave the drippings/fat behind in the pot, and use that instead of oil to saute the vegetables. This will allow the bacon flavor to permeate the dish, overall, a bit more.

Then, either just before serving, or on the side to sprinkle over the served dish, add the bacon or allow the eater to add, themselves.

Moving to answer for OP. If you want to save the crispiness, or a least some of it, the suggestions of sprinkling small pieces at serving time would seem the way to go. It will give you the noticeable contrast and even draw attention to the bacon while not over-powering the base chili flavors. The added bonus that eckes points out is that it gives the option to anyone who prefers to stay away from pork or meat in general to just omit it.

If however you prefer to get the flavor of bacon through the chili, the opposite direction is the way I would go. With things like chowder, many people start with a block of salt pork or slab bacon. I like the smokiness, so bacon for me. Toss that into your pot first and start to saute it,that is make it your step 0. If too much fat pour off some. Then saute your onions and aromatics in that and go from there. When done or well along, pull out the meat. If you want it back in, chop into small pieces and return it, but it will not have a crisp bacon texture. Small pieces will keep if for being off-putting though. This should get you a deeper flavor that permeates the chili.

You could in fact combine the two, use the slab to create the flavor base, then add the crumbles just before serving to accent and provide the texture.

I'd say you need to cook the bacon in step one with the onions, peppers et all... don't use any other oil, just let the bacon fat render out.

I recommend first cutting the bacon up in 1/2 inch (1 cm) squares rather than leaving it in whole pieces (so it's more similar in size to the onion pieces).

This won't necessarily prevent it from being soggy... the only way to prevent soggy bacon is to not put it in at all but to put it on top. There's too much moisture in the chili to keep the bacon crispy. Cutting the bacon into small pieces will minimize the gross appearance, though and will help it blend in a bit more.

All that said, if you have a lot of flavor in the chili already, I don't know that you're necessarily going to get much from the bacon... it's a flavor that likes to be the star and not compete with other similar flavors... and I don't think that chili is the place for that... but that's just me.

You might be able to help emphasize the salty/umami flavor of the bacon by adding some soy sauce, which I find to really help my turkey chili taste more like beef chili.

Fry the bacon separately and let it rest on a plate with kitchen paper.

When your chili is done, sprinkle the bacon over the individual portions while serving.

Your bacon will be crispy and you'll notice the bacon bits during eating.

This has also the advantage that you could invite your vegan friends for dinner and share the chili with them.