What about everyone else?
Here is a list of problems that could occur if a minority population (or majority disenfranchised population) can't, or won't, 'upgrade.'
Class friction
'Upgrading' to a robot isn't free. It requires quite a lot in the way of resources and expertise. So, ostensibly, some people can't afford it.
How do these people react to being surrounded by nearly immortal rich people?
How do the nearly immortal rich people treat these organics?
Keep in mind, fully organic people can still have children, while ostensibly, the mechanical population can't.
Income disparity
Given a hundred, or two hundred years, an effectively immortal human could accrue an enormous amount of wealth relative to someone who only has a working lifespan worth of wealth to draw from.
Even assuming they're not interested in building a financial empire, a mechanical human's operating costs are just so much lower than a standard human's. They have no need of food or shelter, or possibly even transportation.
They don't need to sleep, either, and they don't feel fatigue. They can work 80 weeks and still have plenty of time for hobbies.
Seeing this, the income gap between mechanical and biological humans must be extremely severe, and the wealth gap between them will only grow as time moves on.
Medical Treatment
At what point does it become more cost effective to simply replace a failing human mechanism with it's mechanical counterpart? What happens to anyone who can't afford that? What happens to medicine in general if the solution to most medical problems is just replace the part? Would anyone bother training in how to treat diseases, infection, or any manner of other medical conditions? Even if the knowledge doesn't become lost, the skills and practices might be.
What does that mean for people who haven't, can't, or won't become mechanical?
Disease and pollution
An largely mechanical populace no longer has any incentive to maintain basic sanitation. Machines don't catch colds. Similarly, toxic substances no longer pose a serious threat to a large percentage of the population.
Why bother addressing these problems if they're a non-problem for most of humanity? Or, at least, most of humanity that donates to political campaigns.
What does that mean for anyone left behind?
Food and agriculture
Making sure everyone stays fed requires a lot of people working together. At what point does the economy that supports world wide agricultural industry start to collapse?
Note, currently, in order to make agribusiness profitable, most governments make heavy use of tariffs and subsidies.
A minor sea change in how important governments believed these programs to be could cause widespread famine among those who are still biological.
Workplace safety and labour laws
Tons of people are now made of metal and don't need to sleep.
Also, lost limbs are replaceable.
This may cause drastic shifts in what is considered an acceptable amount of money to spend on ensuring occupational safety and reasonable working conditions.