Should I give out model solutions to exercises
If you don't provide model solutions, it is fairly likely that one of the more advanced students will end up providing their answers to the other students. It doesn't count toward the grade, so it wouldn't be helping someone to cheat. And most of these students will be friends from being in the same courses many times. So a different way to frame it would be, would you prefer: (1) your solutions - that you know are correct and you can highlight the key conceptual steps or (2) whatever the student writes.
Can you provide a skeleton of the steps? This may also help with the tutorial engagement because you could ask the group which steps they were able to complete, for example.
How can the students know if they have solved an exercise correctly?
Eventually your students are going to leave university and apply what they have learned in your class in their new jobs. When that happens, there will be no solution manual. Better to learn now how to convince themselves that the solution is correct. They are being trained to become the experts, to become the ones that write the solution manual.
Now, your course should give them the tools they need to convince themselves that the solution is correct. You should also clearly communicate that practicing these tools and learning how to deal with uncertainty is an important learning goal of these exercises.
How can the students know if they have solved an exercise correctly?
I have to confess that I underestimated this one. I always thought that in mathematics one knows when one has proven something, but many students obviously don't. However, that is what the tutorials are for. It might be relevant to add here that the tutorials are happening via zoom, and the engagement, so far, has been pretty lacklustre. Many students don't switch on their mic or camera, and about 1/3 of them show no signs of life through the entire tutorial. Certainly, the percentage of students that say "I would like to see how this question is done" is much lower than of those complaining about the lack of model solutions.
I am currently a Master student in mathematics and have a slightly different take on it. I do agree that students have to learn how to deal with a scenario where there is no solution given to you, especially if they want to go into academia. However not everyone wants to do so. A lot of them will end up in industry in insurances, banks, whatsoever. These approaches are not as necessary there.
Further, it depends strongly on how advanced they are. I remember that it took me quite a long time to get a good intuition on whether my argumentation/proof is right or whether it lacks precision. This can be learned far more efficiently if you have model solutions at hand. If this is the case also the tutorials will be only of little help because students barely know where their problem is.
Last but not least, a lot of teachers expect their students to spend a lot of time on trying to solve exercises. The students on the other hand have several subjects and therefore only limited time and energy resources which sometimes cannot be spend this way - at least not by everyone. Unfortunately not everyone is on the level of Oxford students, nevertheless one should have the opportunity to learn something. Just imagine, some people have to work besides going to university in order to finance the latter. Their life gets much harder.
You said you consider yourself a pedagogue. However one could also consider you a service provider - this identity heavily depends on the question whether students pay fees for the university. If they pay a lot of money, I think they are right to expect a certain service, no matter whether you think this is pedagogically irresponsible.
After all, why don't you find a compromise? Give out model solutions for some basic tasks, and let some advanced exercises open. Or provide the model solutions only every second week. I think a black/white solution is certainly not the best and a good compromise could be the best way for all interests.