I also do this, but more because it's easier to remove the water than to later clean up the limescale and mould resulting from leaving it wet. Hadn't considered the sustainability angle - my gut feel was that this would be small, but you piqued my curiosity.
This is a long answer, but the summary is: it might make a bit of difference but it's going to be pretty small.
Some unscientific experimentation in my shower (keep your mind on the issue at hand please) indicates that you get roughly 20-30ml water per m2 left on vertical surfaces after a shower. That's equivalent to an even layer of 30μm which sounds plausible, if on the low side. It's probably safe to say the true value will lie between 10-100ml/m2.
The effect of leaving this water in place rather than pushing it down the drain is that it will slowly evaporate. Evaporating water takes energy (in the form of heat), and you are then going to need to remove the damp air by ventilation, which will waste further heat - unless you have heat recovery ventilation installed. How much heat?
The latent heat of evaporation of water is 2260 kJ/kg. Let's say we have 6m2 of shower surface. That gives 180ml of water; evaporating that will cost about 400kJ or 0.1 kWh (all rough numbers). One shower a day for year then gives 400k * 365 = 146MJ per year.
Now for the extra ventilation. From experience I guess that you might need to have a 0.1 m2 window open for an extra hour to dry the shower if not squeegeed. Converting the formula on this site to sensible units, that's about 2kJ per deg C difference in inside/outside temp. Let's say it's 10 degrees colder outside than in; then ventilation loses 20kJ per shower or about 7MJ per year.
Total is roughly 150MJ per year for each daily shower.
Assuming the heat for that comes from natural gas at approx 63 kg CO2e per GJ then that's equivalent to about 9 kg CO2 per year. For context that's roughly equivalent to driving 70km in an average family car, or about 0.1% of the average UK carbon footprint.
This is a really rough guess and could well be an order of magnitude out.
In practice I suspect this is an overestimate: during the Summer months the heat is unlikely to come from your heating; even in winter some of the heat will come from the already warm water rather than space heating; some of the water vapour will condense elsewhere thus releasing the heat back into the house; some of the water would eventually trickle down the drain anyway even if not squeegeed; you need ventilation anyway to remove the (vastly greater) quantity of water evaporated from the actual shower; etc.
Your question mentioned effects on the lifespan of the shower. Water is unlikely to have any effect on durability of the glass:
Glass is one of the most durable construction materials, substantially
resisting the effects of normal weathering for decades...monolithic
glass, [which,] if not physically damaged, has an infinite lifespan.
Plastic sanitary ware is generally made of acrylic (PMMA) over a glass-reinforced polyester or polypropylene former. I couldn't find any data on how water affects longevity of PMMA, but again acrylic is specficially designed and used for applications involving contact with water so the small additional immersion time from not removing excess water seems unlikely to make any difference.
Where the extra water will make a difference is in more porous materials such as silicone sealant, grout and plaster and wallpaper nearby. Extended periods of damp conditions will cause mould growth which, once it has set in, is often impossible to clean off. That said, these are all materials used in relatively small quantities: e.g. replacing a couple of metres of silicone sealant is a negligible amount of additional material over the total amounts involved in a whole bathroom.
The one area I can think of where leaving a shower wet could significantly affect longevity is where non corrosion-resistant fixings (screws, brackets etc) are used. If these corrode it may mean large items have to be replaced. Hard to quantify though, and very dependent on the quality of the bathroom and how well it was installed.
In summary, I would say that removing this excess water will make some difference to environmental impact, but not a huge amount. I think the real choice is between a little bit of maintenance every shower (squeegee) vs. a lot of maintenance (scraping off limescale, scrubbing grout, replacing sealant) at longer intervals. I know which I prefer!