Is slight sagging in my deck railing normal, or am I missing something serious?

That dip you're seeing on the main joists is likely settlement, which can be completely normal, but the ledger board concern is what you really need to focus on first. If the mounting bolts are corroding or the framing behind it is pulling away, that's where the catastrophic failure will happen before the deck even sags anymore. Most settling is acceptable, but a noticeable dip combined with a loose ledger is a recipe for something much worse down the line. Because the ledger is the critical connection to the house structure, that is definitely the priority over checking the joists right now.

Since you're uncomfortable doing professional work, start by systematically checking the attachment points on that ledger. Look for signs of pulling away, not just just rust on the bolts. If the flashing where the ledger meets the house is compromised or has been leaking for a while, that could have caused wood rot underneath the bolts, which is the biggest structural killer for decks. When you inspect the ledger, see if any of the bolts have signs of loosening, which often happens when the wood they are gripping expands or contracts over seasons. You can try tightening them, but if they just spin, you've got a real anchor issue. If the ledger itself looks sound but the rest of the area is dipping, then you'd need to shift your attention to the footings. If those footings are just settling, the joists might just need cribbing or leveling if the post holes allow it. But without knowing what caused the ledger to feel loose, don't start digging around the posts yet. Focus on the attachment point to the main house frame first.

I would suggest looking at the actual wood where the bolts enter the ledger structure, because even if the bolts themselves are tight, the surrounding timber could be suffering from compression or sheer stress from cyclical loading. This type of minor deflection can cause the wood fibers around the connection point to wear down over time, compromising the joint's ability to carry future weight. Have you managed to observe any discoloration or splintering immediatly adjacent to those mounting hardware points?

I've seen this a hundred times on job sites. It's not just the bolts that matter; it's the fastener type and how the wood is reacting to the moisture behind it. When I was framing a large deck last summer, I found the contractor was using standard lag bolts, and I insisted we upgrade to 5/8 inch carriage bolts for the ledger attachment. The carriage bolts actually handle the shear stress much better than the lag bolts do under cyclical loading. You should inspect those holes specifically for any splintering or splitting right where the bolt passes thru the deck board. If the wood is allready splitting, tightening the bolts isn't going to fix the problem, and you need a structural carpenter involved.

If those holes look clean, then your settling concern is likely related to the entire foundation shift rather than just the ledger attachment. If the footings are shifting, that means the entire structure needs re-leveling from the ground up.

I remember when my friend had to replace a support post for his patio, and the settlement was minor but consistent. He ended up using a specific quick-set epoxy foundation mix under the base of the new post instead of just pouring concrete around it. That material really made the difference in keeping the wood from shifting or twisting even when the ground wasn't perfectly stable.

If you're going to start investigating the footings, seeing if that soil around the base is draining properly is key. Sometimes the post itself isn't failing, but the moisture wicking up from the ground is compromising the wood right near the ledger connection, even if the bolts look tight.