It is a "simple" sentence, but I can't find any information how I should parse and interpret this part.
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Do you already know how to make a comparison using ほう and より in Japanese? If not, please learn it first.
The sentence in question is an extension of this. While there is no explicit comparison target marked with ～より, this ほう still means "comparatively" or "relatively".
Despite my appearance, (if one has to categorize me either as a cautious or as a careless person,) I'm comparatively a cautious person, you know.
I'm a more cautious person than I may look, you know.
これでも (literally "even with this") is a set phrase, "although you may think otherwise" or "although I may not look like it".
- このケーキは甘いほうだ。 This cake is relatively sweet.
- 私はよく寝るほうです。 I'm relatively a good sleeper.
- あまりテレビは見ないほうです。 I'm not a kind of person who watches TV often.
方(ほう) is used to make comparisons.
用心深いほう means "the more cautious one".
Examples from プログレッシブ和英中辞典:
4 〔比べられる物の一方〕a side; a part
Give me the smaller one.
The fault was mine.
There was no dissatisfaction on his part.
All of us sided with him.
I am better off than I used to be.
and from デジタル大辞泉: