Pessimistic assessments of the future of wild animal suffering seem to involve a couple ideas: (1) humans are going to continuously rely on natural ecosystems on Earth, and (2) humans are going to terraform other planets. But both seem incorrect:
Natural ecosystems will be replaced by optimized systems, and this will impact welfare
As humanity's economy and population grow, they will replace wild habitats until they bump up against Malthusian or other limits. (Some would say this is already happening, though I doubt it.) But this isn't an 'end state'. First, we can expect a transition of natural life towards more human-supporting organisms. Removing native species, introducing invasive ones, genetically engineering them, etc. These can all be done for reasons that improve the safety and capacity of human society. There will be basic economic motives for transforming ecosystems into being more productive and efficient.
But when people take actions as long these lines, we will place ourselves in a closer relationship with nature. Since we are actually introducing and modifying organisms, we will perceive more responsibility for their quality of life. Of course it won't be adequate - look at animal farming - but there can still be more pressure to improve over the status quo of wildlife.
With further changes, ecosystems might be continuously dismantled and replaced with specialized populations of organisms which are oriented around human society. Examples could be dedicated fields of plants and algae designed to maximally filter CO2 or nitrogen, animals specifically trained to clean up garbage, fish specifically designed to bioaccumulate toxins, etc. Since they are more closely and explicitly connected to specific human needs, we're going to be in a closer relationship with them, requiring more continuous monitoring, and this will create a sense of responsibility for their quality of life.
Finally, ecosystems might be replaced entirely by farms and farm-type operations, closely and microeconomically linked with human operations in arcologies for instance. Then we can have a reasonable expectation that quality of life will be positive, as people will have plenty of contact and responsibility for other organisms.
To be clear, in the short run there could be an increase in wildlife populations as deserts and polar regions become terraformed. However, the deliberacy and anthropocentrism of these operations will make us perceive more moral responsibility for the inhabitants in the long run.
Of course there will still be natural parks, but that will be a small proportion of global habitats, and is not worth worrying much about.
Other planets probably won't be terraformed
Terraforming is a staple of space exploration dreams, but I don't know if it makes much sense. The best candidate is probably Mars, but it's not possible with current technology. Even when/if it becomes possible, it will be extraordinarily costly.
I would give a 60% chance that we will actually send spacecraft to settle a readily habitable exoplanet/exomoon before we broadly terraform a Solar System body to be human-habitable. It simply seems to have a lower required investment and a higher payoff. It's worth noting that the physics of space exploration make it perfectly reasonable to take long leaps before short ones; you don't really need to build a base on the Moon, work up to a base on Mars, etc to explore. In the extreme case, we could directly send probes through intergalactic space right to the edge of the reachable universe. (Though with manned spacecraft, star-hopping would be much preferable.)
If we reach readily habitable exoplanets, there will be a high likelihood of existing lifeforms. If we colonize and control these landscapes, we can reorder them along anthropocentric lines as discussed previously, and again will be likely to take moral responsibility for their quality of life - while probably reducing their population size with our settlements.
In the very long run, conventional terraforming can become a productive pursuit, except then it will start incurring a huge opportunity cost. To put it simply, using a a whole planet to support one thin biosphere on top is a gigantic waste of resources. 99.9% of the rock and minerals on the planet are being used for the sole purposes of generating gravity and stopping cosmic radiation, which could be far more efficiently done with a centrifuge or black hole and a few meters of shell. Planetary mass also creates heat (this is bad, makes manufacturing and computing less efficient, harder to remove waste heat) and risky geological activity. So instead of settling existing worlds, we'll be deliberately engineering new habitats. This won't be like seeding a vast frontier with new life, the new spaces will be specifically and strictly designed for efficiency, with nonhuman life made to closely support human activities. This again will place them in a close relationship where an element of moral responsibility for their well-being will be felt.
Maybe there is some window of time after terraforming is viable but before planetary engineering is viable, where we will see a spread of terraformed wild uncontrolled ecosystems with minimal human oversight. However it just seems like a small fraction of organism-time over the future of the cosmos.