Sister, my heart goes out to you because I think many believers have felt exactly what you're describing.
Elijah looked around and thought he was alone, yet God reminded him that He still had thousands who had not bowed the knee (1 Kings 19:14-18).
Sometimes our isolation is not because we don't belong, but because we haven't yet found all the people God has prepared for us.
I would also encourage you not to assume that being on the outside means something is wrong with you.
Paul was single.
Jeremiah was often alone.
Even David frequently cried out to God from a place of loneliness.
Being in a season where you don't neatly fit into the usual categories of wife, mother, or young single does not make you less valuable in God's kingdom.
The fact that you're newly sober and pursuing holiness is something to thank God for, not something to apologize for.
Sometimes growth changes our relationships because we're no longer walking the same path we once did.
That can feel lonely, but it can also be evidence that God is doing a new work in your life.
As for "what now?" I don't think the answer is to force the next chapter.
Scripture repeatedly calls us to be faithful where we are today rather than worrying about tomorrow (Matt. 6:34).
Keep serving, keep growing, keep showing up, and keep trusting that God knows exactly where you are.
And no, you do not need to get a cat.
You may feel like you're on the outside looking in, but remember that your deepest identity is not "single," "sober," "childless," or "different."
It is that you belong to Christ.
Sometimes God uses these in-between seasons to teach us that His presence is enough before He introduces us to the next thing.
So don't lose heart.
You are not forgotten, you are not failing, and you are certainly not alone.
God has a habit of meeting people in exactly the kind of season you've described.