Joining Two Tables via JSONB column (date)

Given the following data:

create table datas (id int, data jsonb);

insert into categories (id, budget) 
values 
  (1, '{"2022-07-01": {"budget_amount": value1, "some": "thing1"},"2022-08-01": {"budget_amount": value2, "some": "thing2"}}'), 
  (2, '{"2022-08-01": {"budget_amount": value3, "some": "thing3"},"2022-08-01": {"budget_amount": value4, "some": "thing4"}}');

insert into transactions (id, transaction) 
values 
  (1, '{"vendor","equalto.categories.id2",amount, date}'), 
  (2, '{"vendor","equalto.categories.id1",amount, date}'),
  (3, '{"vendor","equalto.categories.id3",amount, date}'), 
  (4, '{"vendor","equalto.categories.id2",amount, date}');

|id|budget| |--|------| |1|{"2022-07-01": {"budget_amount": value1, "some": "thing1"},"2022-08-01": {"budget_amount": value2, "some": "thing2"}}| |2|{"2022-08-01": {"budget_amount": value3, "some": "thing3"},"2022-08-01": {"budget_amount": value4, "some": "thing4"}}| |id|vendor|category_id|amount|date| |-|-|-|-|-| |1|vendor|equalto.categories.id1|amount|date| |2|vendor|equalto.categories.id2|amount|date| |3|vendor|equalto.categories.id3|amount|date| |4|vendor|equalto.categories.id2|amount|date| For a particular category I'm looking to do something like the following:

SELECT categories_id, DATE_TRUNC('month',transaction.date) as tmonth, SUM(transactions.amount),
       jsonb_path_query(budget.data, '$.*.budget_amount') #>> '{}' as budget_amount
from categories, transactions
JOIN tmonth on jsonb_path_query(budget.data, '$.keyvalue()') ->> 'key'

|Category ID|Month|budget_amount|spend| |:--------------:|:------------:|:------------:|:------------:| |categories.id|DATE_TRUNC('month',transaction.date)|budget_amount|sum(transactions.amount)| Essentially I'm looking to join the top level key in datas (first of the month in YYYY-MM-DD format) to the column date (timestamp) in the transaction table. The goal being to get per row the budget.id, month as YYYY-MM-01, budget, sum of monthly transactions for that budget.id Issue being that I can't figure out how to join the two tables on a jsonb column. Could someone please recommend a way to combine this data? Any help would be appriciated.