28M and I can smell the talks of the impending marriage soon and I need advice

So, I am 28, a Ph.D. student here in CS at one of the top public institutions. I am in my 2nd Year and will be in 3rd before I turn 29. I recently had a fallout with a fellow Ph.D. scholar in my college, and that was hard, so I am not holding my breath to find someone now through dating. I recently turned 28 this September, and my parents told me they would discuss the marriage situation, so this is where I stand.

Although I am at my ripe age and they can't force me, I would try to be upfront that I am not looking for marriage before my Ph.D. in all proportions. The Ph.D. currently is stressful to me, and with the baggage of anxiety issues that have stayed with me since childhood, I can't realistically be a partner to someone for now. Furthermore, I want myself to be stable so whoever my partner is doesn't have to face the uncertainty related to the future. I plan to tell them that while I won't disagree with meeting people they want me to meet, I won't commit until I see myself standing firmly on my two legs, and this I would tell her too, if in case I like someone.

Finding people after 30 becomes a little complicated than 20s, and there is some tiny possibility that I may be alone forever. Still, this is the worst case I am willing to accept compared to marriage now.

Otherwise, I consider myself a cheerful and kind person by heart, and despite my introverted nature, I am pretty social and have many friends from both genders. While they might not replace the status of a partner, it does help me a lot as I don't feel lonely. Furthermore, I occasionally love my own company, too. I consider myself a whole person which doesn't require much external. This gives me hope I may survive the period of uncertainty.

What do you think regarding my decision to be upfront with my family?