TL;DR: I second Barnlifter’s recommendation to do a general warm up first.
I’m a masters lifter too. Some days I feel more creaky and stiff than others, especially if I’ve been pushing intensity and/or it’s winter. (I train at home in the garage and it can be pretty chilly, which seems to exacerbate the creakiness.) If I can avoid it, I try not to train first thing in the morning.
While specific “mobility” work is typically frowned upon in the BBM community (because there isn’t evidence suggesting it’s helpful), you aren’t wrong for trying to figure out what works for you.
Before I found BBM, I trained at a gym and my coach had me doing all kinds of static stretching, foam rolling and mobility drills before lifting. He probably learned in college that old folks needed it. Did it help? I doubt it. I don’t think there was any special magic or benefit. It was probably just a waste of time.
One of the best things I do for me is go for a walk in the morning. 10-15 minutes, maybe longer if the weather is nice and I’m not in a hurry. I either go around the block once or just up and down the street a couple times. Nothing brisk. It’s a stroll. I take my coffee with me. I call this either “busting the rust” or “walking the dog.” If nothing else, it puts me in a better mood than sitting down in front of a screen.
Prior to my training session, I don’t do any specific mobility work. I start with a 5 minute general warm-up, usually on the rower if I’m lifting, or I jump rope on GPP days. I never skip a general warm up even if I feel good. I start off gentle and work my way up to about an RPE 6 or 7. Before this, I get everything set up equipment wise for my first lift. Once I’m done with my general warm up, I go straight into my warm up sets unless I do barbell complexes first. (Seems like spending 5 or 10 minutes between the general warm up and starting the specific movement warm up setting up equipment would negate the benefits of doing the general warm up in the first place. I do stop for a couple seconds and pull up my knee sleeves between the rower and the rack. That’s all.)
If I’m feeling especially stiff, I do a set of barbell complexes with the empty bar in the 8 to 12 rep range. (RDL, bent-over row, front squat, overhead press, back squat, good morning.) I don’t do these really fast or really slow. I control the bar speed throughout and focus on feeling the ROM.
Then I do two sets with the empty bar for 10 to 20 reps before I start adding weight.
Depending on how stiff I feel, my first couple of warm up sets are with minimal weight and I keep my jumps small. If someone wants to criticize me for doing a set or two of “junk volume,” that’s fine. At that point, I’m almost always feeling limber enough to proceed.
All of this would just be for the first movement. Warm up sets for the remaining movements are more straightforward as I’m usually feeling ok by then.
So all that to say, it doesn’t need to be complicated. It should be relatively specific to the movements you’re training that session. But if you find that doing something less specific works for you, then there isn’t likely to be any harm done unless you’re static stretching. I wouldn’t recommend that.
I’m also not recommending you adopt my warm up routine either. This is what I’ve found works for me. It’s evolved over time and will likely continue to do so.
All that said, if you think you might actually have a health concern, I’d suggest discussing it with your healthcare provider. Of course, we all know as lifters that most healthcare providers aren’t half as smart as the good doctors here.
Finally, if you aren’t using knee sleeves and elbow sleeves, you might consider it. I don’t always wear mine. But they do feel good, which is nice especially when I’m not feeling so good.
Hope something in all that is helpful.