How to get SvelteKit forms working in Vercel/Netlify/etc - deployment

Question

I'm pretty new to Svelte but it is nice and straightforward in general with this form submission I have spent hours and it is driving me crazy as it doesn't make any sense why it is not sometimes working in Vercel.
I created a separate minimal SvelteKit project that submits the form to this webhook.site endpoint and it works perfectly in localhost but in Vercel deployment it works sometimes. Works once, then doesn't work three times, ten works four times in a row, then doesn't work again. Random. Sometimes Vercel gives an error, sometimes not. Here's the error:
[POST] /?/create
22:12:29:53
TypeError: fetch failed
at fetch (/var/task/node_modules/undici/index.js:105:13)
at process.processTicksAndRejections (node:internal/process/task_queues:95:5) {
cause: ConnectTimeoutError: Connect Timeout Error
at onConnectTimeout (/var/task/node_modules/undici/lib/core/connect.js:176:24)
at /var/task/node_modules/undici/lib/core/connect.js:123:46
at Immediate._onImmediate (/var/task/node_modules/undici/lib/core/connect.js:164:9)
at process.processImmediate (node:internal/timers:471:21) {
code: 'UND_ERR_CONNECT_TIMEOUT'
}
}
Then, without doing anything I tested again and it was working like 20 times in a row. I left it like that and came back after ~1h and it was still working like 10 times per row. I was here.
Then I decided to start experimenting again and in the next commit I removed the header authentication that isn't needed for the webhook.site but I had it there because, during the endless hours of hassling with it, I got at some point "feeling" that if the not used HASURA_ADMIN_SECRET ENV variable is there then it works more often. I know it is nonsense. It stopped working for good. Tested at least 20+ times with some breaks to be sure. Also tried multiple other endpoints that work brilliantly from a simple PHP script I created, from reqbin.com or from Postman. I have tried everything.
Allright, then I thought I was right - that magical HASURA_ADMIN_SECRET is needed so I added it back. That didn't fix the issue. Tried dozen of times and then although I made sure I added that header auth back properly I decided also to roll back to the version where it was stable working for so long as seen here. Now even that doesn't work anymore.
I tried long ago to deploy to Netlify and CloudFare, too as I suspected it is Netlify issue but I failed to even get the site working. So I decided to spend more time on getting it working in Netlify and when I got it working I got exactly the same error as in Netlify https://i.imgur.com/repNxyf.png so here's my dead end.
(I will make this post shorter once I get sorted)