So sorry for your losses. No it’s not guaranteed to be egg quality. Maybe if it had been 1 isolated miscarriage. 4 miscarriages points to an underlying issue. Egg quality is just one possible cause, and there are so many we don’t know about.
Statistically only 1 in 100 women will have 3 or more miscarriages. If you have 1 miscarriage you have the same statistical chance of having a second as most other women - about 20%. If you have 2 miscarriages it rises to 28%. If you have 3 though it rises to about 43% chance of having another miscarriage for each subsequent pregnancy. It’s not the miscarriages that increase your risk - it’s the fact there’s probably an untreated condition.
You need to be referred to a recurrent miscarriage clinic asap. The criteria is normally after 3 miscarriages, but as you are over 35 many accept after 2. Get onto your GP. They will arrange tests and try to identify a cause. (Edit I see you are waiting - cross posts. If you get pregnant while waiting, phone them - they will often try to get you in)
I had 3 miscarriages between the ages of 36 and 38, before being diagnosed with a blood clotting issue. They were blamed on my age, weight, I ate a bad oyster, bad luck, these things happen etc, when a simple blood test would have identified the issue. I could have been 25, a perfect 10, eating only organic and have 4 leaf clovers sprout under my feet everywhere I walked and I would still have had these miscarriages as my blood clots too easily. Treated with aspirin and heparin, I had a successful pregnancy at 38, then another miscarriage, and a second successful pregnancy at 41 with progesterone added.
Good luck x