Hi OP, we were in this situation in 2019.
We had cash, no chain, were out of our minds living with family and desperate to move in.
Were assured repeatedly that elderly vendor was moving in with her daughter and was therefore chain-free, could move as fast as we wanted.
After a month or so of inexplicable delays, it turned out she was actually moving into sheltered accommodation - which wasn't vacant yet. So was dithering around waiting for her side of the 'chain' to be available.
I sent a cold and factual email to the EA and both solicitors, copying the (thankfully written) confirmation that she could meet our timeframe becasue moving in with family.
I said that since our offer was dependent on the facts as stated, we were going to drop our offer price by £X,000 per week that the delays continued, starting the following Monday.
The EA called me saying I was being outrageous (!) but I said the offer price reflected our timeframe being met and that, outrageous or not, I was going to proceed as outlined in my email.
Lo and behold we moved the following Monday! She did as she'd promised and moved in with her daughter until the next move was ready. I guess it cost her double van rental but we were paying a fair price for her house and being lied to, so I had zero sympathy.
In your shoes, I think you should decide if you want to proceed at all, and if so what you want that to look like (lower price incrementally for each delay? or just make a lower offer given the chain?)
There's no reason you can't keep looking at what else is available while you decide this. Best of luck.