Welcome to NGA, kat1953. No, I would not recommend that just yet. Please display or comment where are you located (city, state) and your usda zone.
Hydrangea rejuvenation pruning involves pruning the stems in stages during times when the plant is dormant. For example, you can cut the longest 1/3 of the stems one winter, the next 1/3 longest on the following winter and the rest on winter #3. Because this much cutting is stressful, it is best left for times when the plant is dormant.
Depending on where you are located, you should avoid pruning a hydrangea macrophylla now at all costs: they developed invisible flower buds from either late Summer 2020 or early Fall 2020 and then these buds open ahywhere from Spring 2021 through as late as Summer 2021. So pruning now cuts off the flowers for 2021. A hydrangea macrophylla should be pruned after it has ceased to open flower buds but before it produces invisible flower buds in 2021. The normal time in my area for developing new flower buds is somewhere in July so I try to be done pruning before the end of June. In areas north of me, that happens later. In Florida, it happens earlier.
The normal time for opening blooms depends on one's geographical location. The further south one is located, the earlier the plants can bloom. Flower buds start to open here around late March to April but they can open as late as summer in places up north.
However, you can deadhead any leftover spent flower at any time. This, however, is not the same as pruning.
Picture 2 shows some late frost damage but the other two pictures do not show any issues. Dead wood (stems that do not leaf out at all) can be removed at various times based on your location. I usually wait until May to remove dead wood (you can prune stems that do not leaf out all the way down; or you can prune partially those with dead wood only at the end of the stems). I would not prune the stem in Picture 2 as it is leafing out at the ends right now.
If your plant typically does not bloom, consider these causes:
* damage from pests like squirrels, bunnies or deer (you should see where they nibbled)
* pruning at the wrong time (prune only after the plant stops opening blooms)
* late frosts zapped either the flower buds or the stems when the plant breaks dormancy early (winter protect or do not fertilize early)
* winter was too cold so the plant may need winter protection on a regular basis or switch to hydrangea paniculata and arborescens cultivars (your old stems from last year are leafing out so this does not seem to be the case)
* applying fertilizers late in the growing season (this can keep the plant in "grow" mode, just as early frosts arrive and kill flower buds or stems)
* use of high nitrogen fertilizers (this produces lots of nice green lush plants with no or few flowers); watch out for some Micracle Gro formulations with N of 30 in their NPK Ratio.
* established hydrangeas are not hungry feeders like roses so feeding them by letting 2-4" of organic mulch decompose is enough. You can also apply a single annual fertilizer application. But of course, you may need to amend the soil to acidify it (if your soil is alkaline) more regularly. For a plant of that size, you can use a cup of cottonseed meal, organic compost, composted manure or a general purpose, slow release, NPK 10-10-10 chemical fertilizer (per label directions or at half strength). Exceptions: if your soil is deficient in some nutrients (like sandy soil) or when growing in pots. You can use weak fertilizers like liquid seaweed, liquid fish, coffee grounds throughout the growing season but discontinue them three months before your average date of last frost. In Spring, you can fertilize after your average date of late frost.