How to get your employer to "allow" you to work outside your main gig that is in the same field?

the real question here is why do you want to establish a side gig in the same field as you current employer who is paying you to do that for them?

i believe most here do have side gigs, but in alternating fields than where they are employed in. and no, "online" is not a field, but a medium. so if your employer sells b2b leadgeneration forms (as an example), i would personally not do that as a side gig. selling b2b workshoes on the other hand, is an entirely different thing.

You need to just go ahead and build it. If you wait for permission, your idea will stagnate and you’ll talk yourself out of it. You’re very unlikely to build / develop something that will directly impact or scare your current company.

Don’t be stupid about it - writing code for your idea while at work is obviously not something you should do. Handling support calls while “on the clock” is also a bad idea.

Perhaps work on this project through a cut-out? Have a friend start a company (of which you are majority owner), and work out a deal where your friend will get a small cut in return for being the “face” of the new project?

(sorry for a long and scattered unfocused post but I know what you mean with that silly contract part that is almost 100% standard industry wide with draconian scopes.. not a lawyer, should probably talk to one that's on relevant local)
How about we play this out as imaginary case...
I'll assume your not working to actually compete with your employer.
You start working on your side project.
If you let your normal work be affected, sure they should be able to fire you, but I'll assume you keep true to the side project and your work is just as impeccable as ever.
you don't talk with any work acquaintance on your side projects.
You work to build it 6-18 months.
So far no one's the wiser.
You start marketing your cockroach of a project, chances someone work related would find out about it and you are what 1:1,000,000,000? depending on market and such...
You take 3-9 months for even the 1st customer.
After 12-24 months it starts getting some traction.
after 60 months total it's big enough you quit and go full time.
Probably no one's the wiser still when you quit.
At some point you do become successful and your old boss somehow see your name on it.
Will he care to have a claim against you? most likely not, would he even still be at your old company?... if it's a large tech one, probably not..
Ok, worst case he does and the company goes against you..
What can they claim at worst? depending on so many things lets say they want to claim your entire company and all the wages you have been paid working for them.
Surely you get a lawyer and this drags for a few years, meanwhile you run the business as usual? or diversify further into something they can't get a claim on?
I have a feeling what would actually happen is some compromise and you pay out some part of your company's worth.
You'd probably be happy at that point. And your new life would just be cemented...
(Don't confuse contracts and claims from validity and don't think there is a single objective answer to most things or that lawyers or judges are objective...
Most cases aren't like TV, they try offers and counters to get something partial and even the Judge basically doesn't wanna read and/or listen if he can pressure the sides to talk and/or agree on something without him.. lawyers get paid more to drag things on.. both sides usually end up losing money from that interaction over negotiating something..)

I know this is a bad advice from many aspects..
What's the risk of not trying? not ever having any chance any anything better?
This industry standard of contracts saying almost 'we own you and your thoughts for well after you finish this contract' is outrageous to me, yet I got nothing to do with that either.
Not anything written in a contract has legal validity.
I nickname these 'scare articles'..
I can write anything I want into the contract.
Until we fight it out in courts no one knows if it's valid.
And that's expensive to do.
I wish there was repercussions for highly invalid things to be put into contracts.
Depending on where you argue these out, sometimes the higher level rule is that employment can not be restricted. (not to counter stealing business secrets and/or assets and such)
You can go talk to a lawyer, that will give you relatively valid advice or even start one on a retainer if you'r serious.
Once I had a boss agree to sign off on a specific exemption, there are easier to talk about before signing a contract, "I just want to make sure you don't have a problem with me keeping my side projects.." he'd usually ask what they are about etc.. and if they aren't too closely related, he's probably not think it's an issue.

So the contract says you cannot sell products similar to the ones your employer is selling? Or that you cannot work as a developer while working for them? It would seem unfair to stop you from programming software for yourself.