If you want a nice assisted-opener for that kind of budget, your only manufacturer choice is Kershaw, which is what I buy exclusively now.
I would recommend the Kershaw Leek.
It's probably cheapest on eBay, as there are plenty of them to choose from there.
14C28N steel is pretty good.
Unfortunately, assisted-openers with better steel generally sell for a premium that's above my budget.
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Here's a thread that's all about my favorite knives, though I think the Leek is the best fit for your needs:
https://budgetlightforum.com/t/-/50173
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There's only one knife that I like more than my Leek, but it's kinda pricey and it has a 3.5" blade.