Alliums cross breeding for seed production?

This year, I planted 3 varieties of onion sets that I hand picked from the bulk bin at the farm store.  I chose storage onions in red, white, & yellow.  In my excitement of having a bountiful garden that was well planned with proper spacing & soaker hose irrigation to make watering easier on me, I ended up losing the vast majority to weed competition/overwatering/rot.  When I realized this, I stopped providing additional water & just let the few that were left to recover on their own, they did, & even bulbed up a little.  My family had grown about 4 rows of onions every year, & they always did well.  I haven't grown them in a very long time, as such, I misremembered some details like water needs & just how long it takes to get them to harvest ready.  Now, those small onions are curing, & I'm going to try replanting in the fall to try overwintering them along with garlic for a bigger/earlier harvest next summer.

My question is, if I allow the scapes to flower, is it possible they will produce seed that can be a hybrid of different types of allium?  My plan is to also plant shallots, hard neck garlic, & soft neck garlic all in the fall.  I'm aware that letting the scapes go can reduce bulb size, but for my needs I can live with that for the larger bulbing onions.  Will red, yelow, white onions cross-pollinated produce viable seed?  Will hard-neck garlic cross with soft neck?  Will onions & garlic cross?  I know these questions only matter for seed saving, but I'm curious to know and maybe others are too?  If anyone knows if this question has come up before, feel free to link the thread.  Thanks!

I'll take a crack at this, but probably someone more experienced will come along with better info. Your bulbing onions of various colors will absolutely hybridize. Shallots are also well-known to hybridize with onions, and I know people who purposely do that with potato onions, some folks don't like the results. You will be extremely lucky to get garlic to produce any seeds at all, and I don't know how easily they hybridize. I suspect the chances of crossing between garlic and onions are vanishingly small, but pretty exciting. You might be interested in this bit at Wikipedia: https://en.wikipedia.org/wiki/Onion#Hybrids_with_A._cepa_parentage

Thanks for the reply!  I read the entire link & learned quite a bit.  The shallots I bought for fall planting are large & healthy, and I chose ones that were already divided into 2 so that I could divide them again like garlic for planting.  This will be my first time growing them.  I bought quite a lot of shallots, hard neck garlic, & soft neck garlic to plant.  Hopefully, they survive storage until planting time.  The main delay for me, is waiting until the rest of my garden is done to place them where I want for next year's biennial seed producers plot.  I don't mind small to medium sized onions overall, because for me they're the right size for most of my cooking with no leftovers.  Long storage qualities are nice as well.  I've never grown any alliums for seed saving before, but as I go down this road of experimental landracing, my curiosity must be satisfied.

Update:  I was able to harvest maybe a hundred seeds from a handful of the survivor seed heads that had already been pollinated by the time I pulled them.  I don't know what exactly they'll produce, but some combination of red, white, & yellow.  I noticed on the flower heads that not every bloom got pollinated, so I imagine these are all potentially outcrosses as in not self pollinated I think.  Now the question of how to plant the seed?  Do I start it in the fall in a pot to let them germinate & make "sets"?  Do I direct sow mid winter or spring?  What have you all done to have good luck with onion seeds?