How do I know if a given hardtail MTB frame is supposed to have suspension forks? I read somewhere that if you want to convert a suspension bike to a rigid you need 'suspension corrected' forks which are longer. So I assume there are different types of frames based on if the forks are supposed to be rigid from the start and another design that is meant for suspension forks (?). If that is true, assuming that I can't measure the slack angle of the frame, how do I know if the frame is designed for suspension forks or not?
Before suspension forks became commonplace, all mountain bikes were designed for a rigid fork. Fork length was sufficient to give good clearance between the crown and tire.
Suspension forks need to be longer than the minimum length rigid fork as obviously they need to compress without the tire hitting the crown. As suspension forks became available, frame manufacturers designed frames with higher headtubes to accommodate the longer suspension forks. Over the last few decades common fork travel length has gone from 20mm to over 150mm, and headtube height has increased accordingly. If you look at modern frames and frames from around 1990 it's easy to see how frame geometry has evolved.
So, one can say that a frame with a moderate to large headtube to axle distance is designed for a suspension fork. Modern mountain bike frames are designed for suspension forks with a specific travel and headtube to axle distance that results in a desired head tube angle. XC bikes have less travel and shorter headtube to axle distance, downhill bikes have more travel and hence longer headtube to axle distance. There are still bike frames that are designed for a shorter rigid fork: many fat bikes and minimalist rigid single speeds for instance.
I believe the term 'suspension corrected' comes from the early days of suspension forks when the previously typical rigid fork length used was shorter than contemporary suspension fork length. To replace a suspension fork with a rigid one, a longer 'suspension corrected' fork was needed to preserve head tube angle. Note that modern bike suspension is designed to 'sag' slightly with a rider on the bike. A replacement rigid fork needs to be the same effective head tube to axle length as the'sagged' suspension fork, i.e. slightly shorter than the uncompressed length.
What you really want to find out is what headtube to axle length and head tube angle a given frame was intended to have. If you know the brand, model and year, do some searching on the web, you might be able to find out what model fork it originally came with and what the length of that fork was. If you know the intended use of the frame (XC, enduro etc,) you can look up common head tube angles and use geometry to estimate the headtube to axle length.
Frames are designed around forks with a particular axle-to-crown dimension, which in the case of suspension forks correlates pretty closely to travel. So it's not just a question of suspension fork or not; it's a question of what the axle-to-crown should be, or how much travel. For example, very early suspension forks with 60-70mm travel didn't require a radical change in geometry from the fully rigid mountain bikes of the day, and could be plugged into them and yield something reasonable.
To the question of how to know what you're dealing with or what to do in the case of a bare frame with no information obtainable as to what it is:
This sounds geekier and more complex than it is, but the best approach is to take all the point-to-point distance and tube-to-tube angle measurements you can from the bare frame, use those numbers to model the frame either on paper or in a simple 2d CAD program (freeware is fine), and then go from there to see what different fork axle-to-crown lengths are going to get you when you plug them in. In CAD this just means you'll be making the model of the frame, then rotating it around the axis of the rear axle as you stick in lines of different lengths to represent the different forks.
You'll then be able to take one of two approaches. If you want to try to figure out the best guess you can as to what the bike came with originally, you can plug in different axle-to-crown lengths until you find one that gets you head tube and seat tube angles (which change with fork length) that both look suspiciously close to cleanly rounded numbers, say 71 degrees up front and 73 in back for a lot of hardtails. Manufacturers tend to design things in a way where if you measure the built bike, those angle numbers are similarly clean. There's not all that many length/travel groupings of forks to work through.
Alternatively, once you have your paper or CAD model, you can just plug in different axle to crown numbers until you get one that results in head tube and seat tube angle numbers that make the bike how you want it, or as a way of getting the longest travel you can that still keeps them within your own metric of what's reasonable, or as a way of figuring out how to work with what you have, etc. BB height, standover, and minimum handlebar height also get affected.
When making the model, remember to include headset stack height as applicable (14mm of lower stack height for an external cup headset, 3mm for ZS, and 1mm for integrated are the numbers I'd use).