0.999... is a number. It's not a series or a limit, it's a static and constant number. There's no "as you add on more 9s," because the number is the number. Just because it may take you time (maybe an infinite amount of time) to write it out doesn't mean it's a different number as you write it.
If I write out 1,000,000,000, it's 1 billion. And it's always 1 billion. It's not some limit that starts at 1, then goes to 10, then 100, then 1000, until we reach 1,000,000. It's just 1 billion. And 0.999... is just 0.999..., which is also just 1.
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0.999... is a number. It's not a series or a limit, it's a static and constant number. There's no "as you add on more 9s," because the number is the number. Just because it may take you time (maybe an infinite amount of time) to write it out doesn't mean it's a different number as you write it. If I write out 1,000,000,000, it's 1 billion. And it's always 1 billion. It's not some limit that starts at 1, then goes to 10, then 100, then 1000, until we reach 1,000,000. It's just 1 billion. And 0.999... is just 0.999..., which is also just 1.