I spent a few years working in and around the Energy industry - including a stint working at a supplier, I'm no longer there so unfortunately I no longer have access to the email chains I had discussing this with legal. The consensus at the time was that a "traditional" i.e. non-half-hourly (NHH), non-smart meter reading itself was not considered personal data - they are conceptually tied to a metering point (which may or may not be a physical meter), not to an individual and don't represent an individual's energy consumption (the granularity of the reading is insufficient to tell anything about the usage profile)
But this information, while all around the implementation of GDPR it was a couple of years back and to be honest it was bugging me that I might be out-of-date on the current practices so I reached out to a former colleague who was the Data Protection Officer at the supplier I worked at to try and get a more up-to-date take. He's since moved on but was there until recently so has more experience with the topic since GDPR actually went into effect.
I asked him whether a) estimated opening reads were considered "personal data" and b) what would happen with a request to change one under article 16 and he had this to say, I've translated industry-speak in square brackets:
a) for NHH ["Non Half Hourly" - meters that are read ad-hoc, essentially all non-smart domestic meters will be this] an estimated reading wasn't personal data automatically until the billing flag was set in CRM and those would be the only ones we'd include on an SAR [Subject Access Request], any others are internal data not personal. HH ["Half Hourly" - meters for higher consumption users, typically larger business premises are billed on increments for each half hour so have readings for each] and remote [smart meter] readings are always personal for domestic and microb [micro-businesses are a certain class of non-domestic energy customer see condition 7A]
b) erm no! we'd only change it if the value in CRM didn't match the value in the D10 [industry Data Flow used to transmit meter reads] for some reason. if they match it's an accurate representation of what we estimate the reading to be so it's just a vanilla billing dispute not a data protection issue so i'd have punted it to [name of person who was head of metering]
From that it would sound as though the estimated read would count as personal data - so long as it's being used for billing purposes, but that doesn't mean they have to accept your read in it's stead.
It all comes down to accuracy - GDPR requires that personal data be "accurate" but provides no definition as to what "accurate" means (which makes sense since you can't give a one-size-fits-all answer that isn't an encyclopedia) and while The Electricity Directive 2019 confirms the need for accuracy in billing again it doesn't tell us what that means. The implementation is left to member state regulators.
In the UK this is OFGEM and all opening meter readings are validated through third parties (so you don't end up with the foxes guarding the hen house!) and are calculated using the following formula:
Last validated reading for the meter point <= supplied reading <= (expected daily usage x number of days since last validated reading x 2.5)
where "expected daily usage" is obtained from a database maintained by the regulator - it's calculated off meter type, property type, property use, previous validated reads etc.
So if the customer provides a reading that falls outside the above the supplier can (and in practice invariably will) reject it as being inaccurate.
Now this is why the when a meter reading is provided matters - reads you provide are always assumed to be the read on the day you give them. With opening reads there's some leeway, I can't remember the official rule on how much but usually they give you up to the next estimated read is generated but more on that later.
Now if the reading you're trying to submit is a "now" reading and it's failed the validation criteria and you aren't happy with the rejection you can force the issue by demanding the supplier come read the meter.
You don't say how long has passed since the opening read - more than the week from what you've said so presumably at least a month (guessing you've had at least your first bill).
Now if they are saying the opening read was X (based on the estimated usage) and you're it should have been X + Y and the current reading is X + Y + Z you want to pay your actual usage Z not Y + Z. What you need to do is dispute the opening read, which you're entitled to do, arguably GDPR of Article 16 gives you this right, but on it's own it's a weak argument. There's established means by which an estimated read's "accuracy" is determined and assuming they followed that they're going to just tell you that as far as they are concerned it is accurate. Any challenge to that accuracy is going to have to be done within the legal/regulatory frameworks for assessing accuracy, that's what they're there for, if they won't accept your reading escalate that to the regulator - and as soon as you can. OFGEM for example allow disputing of opening reads for 12 months - it doesn't have to be resolved within that 12 months it just has to be lodged with them within that time.
If you try and use the GDPR angle to pursue this IMHO it's going to muddy the waters and not help you get what you need - pursue this on billing accuracy.