Possible Nuances of 「まで」 in sentences like these

First of all, I want to apologize for my first attempt at this question (which you can still find down below); however, as others seem to be interested in it as well I will try to make myself clearer:

I first came across the construction of 「お気軽に」 in this sentence:

(1) 秋田の親戚から届いた本場仕込みの醤油お分けしますお気軽に園崎までどうぞ

(from: ひぐらしのなく頃に EP:8)

When I searched for the meaning of 「お気軽に」I came across this article: https://eigobu.jp/magazine/okigaru

Basically, this construction means something along the lines of “feel free to…” (at least here). However, what made me wonder was the following example, mentioned in the article:

(2) 何かご不明な点がございましたら、担当者まで お気軽にお問い合わせください。

As already implied in the comments, the 「まで」in these sentences may just have a spatial meaning (in the sense of going as far as a certain area). This meaning would fit for the first sentence as it is mentioned that the house of the 園崎 family is relatively far away from the rest of the village the story takes place in. Nevertheless, in the second sentence I did not get the impression of this spatial meaning. Here I got the impression that the 「まで」is used to add a nuance of extent independently from place and more in the sense of:

② 動作・作用の至り及ぶ程度を表す。ほど。

(from: https://www.weblio.jp/content/%E3%81%BE%E3%81%A7)

Because of that I got the impression that the second sentence implies something like: “Feel free to contact even the manager” in the sense that it is not usual to call the manager in cases like that.

Therefore, I was wondering if that impression is correct and if not, why is 「まで」used here then? On top of that, would it be possible to use particles (if yes which) in (1)?

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I came across this site, explaining the use of 「ご気軽に/お気軽に」 https://eigobu.jp/magazine/okigaru (It is mentioned that they have the same meaning in the article)

One of the examples sentences additionally features 「まで」in it.

何かご不明な点がございましたら、担当者までお気軽にお問い合わせください。

Another example from 「ひぐらしのなく頃に」

秋田の親戚から届いた本場仕込みの醤油お分けしますお気軽に園崎までどうぞ

Does this 「まで」underline the general meaning of 「ご気軽に/お気軽に」? If not, what exactly does it mean? Does it simply refer to some sort of "spatial" range (in the sense of going as far as a certain place)?