Sounds like you know your Adventure game engines thus the question
I think Wadjet Eye uses AGS, IIRC.
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.)
I've been looking for something that would be akin to Wadjet Eye making games- I' assuming they have an entire template they use and mostly replace art assets although I could be completely wrong. Some of them have very different Stat/etc systems.
Anyway, I just want something fun to dabble on that won't frustrate me too much. I'm familiar with Renpy and have done some work with it but like you mentioned I've overlooked Visual Novels for P&Cs. I guess I could do the conversations/story in twine/renpy and worry about the mechanics of moving around/interacting with a world down the line.
I only know Golang and some python, so the c# for unity was intimidating. I was really hoping to find a decent go game engine but I haven't found anything relative. There is a golang game engine I forget its name.
But since Godot is getting some serious backing these days, give it a few more years and it'll probably be a juggernaut in the space like Blender.
You can test it and see how it works if it's adequate or not for your specific usecase.
