I agree that an ultimatum is not the way forward- you’ll always know it wasn’t something he wanted and that will have an impact on your self-esteem and your relationship with your partner. additionally, if he agrees to get engaged because he feels pressured, it either won’t happen (he’ll agree to engagement but nothing more will happen, unless forced) or the marriage will fail because it is not what he actually wants.
I think you need to decide for yourself if not being married is a dealbreaker- you need to be clear on what it is you want and why so that you can be clear with him. No point going into a conversation about what you want without being clear about what is an absolutely requirement vs what would be a “nice to have” and could be compromised on. Is it the financial security of marriage, is it the visible commitment and expression of love that comes with marriage, or perhaps all of that.
Once you have clarified inn your own mind what you want/need going forward then I think there is no way to avoid having to have that difficult talk about marriage and be clear that it is something important to you, that you thought it was important to him too- he certainly said it was- and you need to know where he stands so you can make decisions about what is right for you. You could start it by writing a letter but ultimately you will have to speak to him face to face about it.
Maybe he has changed his mind regarding marriage, perhaps he was always “future faking”, or possibly he doesn’t feel you can afford the wedding he/you imagined when you made those plans and does not want to disappoint you? Has something changed for him that has put him off/made him wary of marriage? For example, a close friend or family member going through a messy divorce. You won’t know until you discuss it.
FWIW, I think marriages relative later in life can be more complicated re assets- often more have been accumulated before the marriage takes place than if you married in your 20’s, and if one partner brings significantly more to the marriage (e.g. property, savings, investments or pensions) there can be a fear that if anything goes awry in the marriage, they stand to lose a lot of what they have worked for over many years. Of course nobody goes into marriage expecting it to fail, but the reality is that many do, and most people are aware of the possibility/possible repercussions for them financially if that were the case.
I’m not sure i would want to marry if I were single and met someone now (in my early 40’s)- especially if I had significantly more in the way of assets- because of the potential outcome for me and having less time to mitigate/re-accumulate what I might lose in the case of divorce. Of course, them having a young baby does impact on that- but unless OP has stopped working, having a baby will not necessarily have a negative impact on her earning or pension (I’m not saying it can’t, just that it does not have to if she is still working- it made no difference to my career at all). If she is not working, she needs to rethink that plan and go back to work to ensure she is financially secure now and in the future.