At my usual budget (side projects on own time) with no artists I mostly just tinker with dialog trees in Twine or Twine-like languages. (I've got my own finished YAML-based Twine-like and my own unfinished Inform-inspired Twine-like that maybe one day I'll push closer to completion.)
Given a small budget, I feel like you can go a long way with Löve 2D or Ren'Py. (Both were "compile" targets of my YAML-based Twine-like at various points. Which I mixed with some awful programmer art.) Ren'Py especially has a lot of the tools you need to do off-the-shelf Point-and-Click adventures well for a great price and relatively easy learning curve with a ton of examples and tutorials out there to learn. I think Ren'Py's focus on "Visual Novels" tends to get it overlooked for "point-and-click adventures", but even as "just" a prototyping tool on the way to a "proper Western viewpoint point-and-click" it shouldn't be dismissed so quickly.
Given a larger budget and a general desire to use off the shelf tools where I can I'd probably start with Unity as a base today. It has most platforms covered and I like C# as a language and a growing body of "indie" artists have good experience with it on their CVs. I haven't investigated the existing adventure game packages for Unity, but I've heard good things. I've also heard good things about Inkle's Twine-like engine for Unity.
I'm also sort of watching Unreal Engine 5 as a weird dark horse here given enough budget, and that might be a big budget. Some of the stuff that Unreal Engine 5 is doing wouldn't be directly useful in a "point-and-click" in the traditional sense, but has me curious if there's room to explore things like a modern take on the GRIMe engine with off-the-shelf tools. (GRIMe being Grim Fandango's engine for an attempt at 3D adventure gaming.)