How to lower gearing on Tiagra 4700

Shimano's most recent compatibility chart is available here. Note that these are official compatibility ratings. It is fine to exceed official specs by a bit.

At the rear, you can get a 10s Tiagra cassette that has a 34t cog, but it does technically require the long cage Tiagra RD. The issue was discussed here. The short cage Tiagra RD is rated for a maximum of a 28 tooth cog. If you have this, you could install a Wolf Tooth RoadLink to increase its maximum cog specification. You would need to be cautious not to exceed the rear derailleur capacity, or the maximum amount of chain that an RD can wrap.

You could also get an 11s GS RD, but be aware that they aren't officially compatible. In particular, if the 11s system is made with a different cable pull ratio (i.e. the length of shift cable pulled by each shift on the STI shifter), then an 11s RD won't shift correctly. You stated in comments that the cable pull ratio is the same, however.

At the front, you can't simply change the chainrings, and these are expensive in any case. Stock cranksets with Shimano's asymmetric 110mm bolt circle diameter can only handle a minimum of 34 or 33 tooth chainrings. Please don't construe any products mentioned below as recommendations; they are given as examples, and aren't an exhaustive list of options. You should Google to confirm.

Option 1: You could get a sub-compact crankset.

The Praxis Alba crankset can handle 48/32 chainrings. It doesn't appear to handle smaller ones. As stated in the dealer manual, this crankset maintains your 43.5mm chainline. However, this requires a new bottom bracket. For even smaller chainrings, you would definitely need a third party crankset, but many would also require you to change your bottom bracket. For example, the White Industries G30 crankset can accommodate an inner ring as small as 24t. This is a premium option. I'm uncertain about this crankset's chainline. Be aware that many sub-compact cranksets are designed for gravel bikes. Thus, most of them may have different chainlines.

The Shimano GRX cranksets are available in 48/32 or 46/30 ratios and they shouldn't require a new bottom bracket. However, they don't maintain your desired chainline. Nonetheless, I have heard anecdotal reports that people are running GRX cranksets with standard road front derailleurs.

Option 2: Get oval chainrings, such as the Absolute Black chainrings. They claim to have designed oval chainrings with average effective sizes of 48/32t and 46/30t that fit standard Shimano cranks.

The issue is that you may not like them, and they do need the front derailleur to be set up properly. I have heard some users comment that this was more difficult. Their purported advantage is that they decrease the length of the lever arm when your pedal stroke is in recovery phase, and lengthen it during the power phase of the stroke. These are claims only, and I don't believe studies have shown that they are generally effective.

The chainrings themselves are about as expensive as a new crankset, and they don't get you all the way to your desired gearing. However, you would be able to keep the rest of your current setup.

As discussed in the second link to a previous StackExchange post, you will need to be aware not to exceed your front derailleur capacity as well as the RD capacity.