It has a cumulative effect and drives the continual "upgrade" cycle. When you consider the life-time of an average mobile device, and the resources required to manufacture and ship them, it's a not insignificant problem.
>Berners-Lee writes that in 2020, there were 7.7 billion mobile phones in use, with a footprint of roughly 580 million tonnes of CO2e. This equates to approximately 1% of all global emissions
Of course, not everyone is replacing their phones yearly. Another source[2] says the average consumer phone is 3 years old. That works out to 0.33% of global emissions, assuming the phones aren't recycled/reused to developing countries. Even if assume people are upgrading their phones for app/web performance reasons, the impact is far less than 1%.
To be clear, these emissions include the manufacturing cost, which for reasonable users seems to make up ~80-90% of the carbon footprint. The power usage of the phone itself and associated data centres etc is only a small portion.
It's still somewhat surprising that one could attribute 0.2% of global emissions solely to phone power consumption... I would have expected it to be lower.
Compared to a single person's emissions? Yeah sure, but that's because anything multiplied by 8 billion people is going to be huge. The same could be said for plastic bags and/or straws. In relative terms it's absolutely minuscule, and in terms of low hanging fruit it's definitely not the top. You'd be far better off figuring out ways to decarbonize the electricity grid (40%) or the transport system (20%)
I would imagine for phones and laptops the extraction of materials (rare earth metals to make fancy new chips, lithium for batteries,etc) is probably the bigger issue.
Having gotten away from 500+ watt desktops as the standard for light non-gaming computing has been a win in the energy consumption court.
I think there are lots of good reasons to avoid the upgrade cycle but energy consumption of the end device itself probably isn't it. (Embodied energy of the devices, environmental impacts of mining, no good EOL story for ewaste, etc)