I don't know about 'constantly' but I think once you're 8-10 months into a gig it doesn't hurt. For one, it gives you some real data about your market value in case you want to negotiate at the end of the year for a raise/bonus and second, it's just good to keep these skills in practice just in case of a layoff or you want something better. A bit time consuming but I've found it useful.
Maybe its only my gig and my area of the world, but going through the rounds with companies can be quite a grueling process and many recruiters can't explain the exact technical details or give any concrete salary information.
It's hard to just do it to test the waters when you have a technical project and multiple interviewing rounds (which also include live coding, which for me is very stressful).
Any time you've grown in your job and you're not receiving a corresponding raise, is a great moment to look around.
But also: I like change. I notice I'm more productive in the first half year on a project. Almost every project is interesting at first. Not all projects are still interesting after a year or two. When I get bored, I know it's time to move on. Some companies may have enough diversity in work, and enough flexibility to move me around, that can keep growing without quitting, but my experience is that most don't.
But I'm not constantly job hunting; as long as I'm enjoying myself, I tend to ignore other offers.
Sounds a little early for me. I personally wait at least 1.5-2 years and I'd definitely start interviewing as you near your 4 year cliff which incidentally is why I have started interviewing this past month.
Most tech companies give you a large grant when you join, say 16x that vest 1/4 per year so 4x per year. Then, every year after that they usually give you another 4 year grant but usually at about 1/4 the initial one so 1x per year. Thus, your total amount of stock vesting is in this example would be 4 for the first year, 5 for the second, 6 for the third, and 4 for the 4th.
This also gets more extreme with stock appreciation because the first grant being the largest is also the oldest so has the most time to appreciate in value. Me for example, the value of my vesting equity per year will drop 30% once I hit my cliff next year.