If you’re looking for an antecedent for all the she and her instances, consider the quatrain just previous to the one you cited yourself, especially its last line:
And so it is in this life of ours,
A calm may be on the present hours.
But the calmest hour of festive glee
May turn the mother of woe to thee.
Since a mother is always a woman, or at least, always female, you might consider whether it’s the mother of woe who’s spoken of afterwards to figure out who all those shes and hers may be referring to.
I don’t believe your assertion that for a correct translation you need to know the English gender of the noun “the past” is correct. For one thing, you never retain the grammatical genders of words from a source language when translating into a different target language. That wouldn’t make any sense, and it would end up being terribly confusing to read. Everything would “come out wrong”.
So even if English did have grammatical gender (it doesn’t), you would still ignore that in a translation. Because you are translating into Russian—a language which, unlike English, actually does have grammatical gender—you should for your translation choose whichever inherent grammatical gender your noun for “the past” would naturally have in your own language.
The noun “the past” has no grammatical gender in English because English does not have grammatical gender any longer. Old English, an unimaginably (and illegibly) distant language from the one we speak today, still had grammatical gender which it inherited from its ancestral Proto-Indo-European, but that has long ago been cast off from the modern language.
Therefore “the past” cannot ever be feminine in English. It also cannot ever be masculine or neuter, or common or generic.
That’s because those things are not grammatical categories of English words. For categories that might somehow matter, “the past” is not usually countable, and it is never human or animate outside of poetic personification, which is not what’s going on here in Browning’s poem.
It’s not enough for a language to have nouns/pronouns referring to things of a particular biological sex for that language’s words to have ‘grammatical gender’, because grammatical gender is something very different from biology. It’s about linguistic word classes, and here noun classes in particular.
English cannot indicate the gender of a word because words do not have grammatical gender in English the way they do in French or Spanish, German or Russian, Greek or Latin.
In a noun phrase like Spanish “el agua pura” (meaning “the pure water”), both article and adjective must match their noun in inherent gender. Each word in the same noun phrase there has the same matching feminine grammatical gender so that they all agree with each other grammatically. This type of grammatical concordance you see here in Spanish simply does not happen in English, which is precisely why English is held to lack grammatical gender.
In its article on grammatical gender Wikipedia states (with emphasis mine) that:
Although Old English had grammatical genders, modern English is not considered to have them”.
That article links to an article on noun classes with a broader discussion in which we read that:
When noun class is expressed on other parts of speech, besides nouns and pronouns, the language is said to have grammatical gender.”