This is not easy. I took help from this thread generate days from date range and combined it with your query.
So the idea was to get the list of dates from last 7 days then left join these dates with a static amount 0 to the query you have and then finally sum them. This could be used for any date range, just need to change them in both the queries
select
t1.purchase_date,
coalesce(SUM(t1.amount+t2.amount), 0) AS amount
from
(
select DATE_FORMAT(a.Date,'%Y-%m-%d') as purchase_date,
'0' as amount
from (
select curdate() - INTERVAL (a.a + (10 * b.a) + (100 * c.a)) DAY as Date
from (select 0 as a union all select 1 union all select 2 union all select 3 union all select 4 union all select 5 union all select 6 union all select 7 union all select 8 union all select 9) as a
cross join (select 0 as a union all select 1 union all select 2 union all select 3 union all select 4 union all select 5 union all select 6 union all select 7 union all select 8 union all select 9) as b
cross join (select 0 as a union all select 1 union all select 2 union all select 3 union all select 4 union all select 5 union all select 6 union all select 7 union all select 8 union all select 9) as c
) a
where a.Date BETWEEN NOW() - INTERVAL 7 DAY AND NOW()
)t1
left join
(
SELECT DATE_FORMAT(purchase_date, '%Y-%m-%d') as purchase_date,
coalesce(SUM(amount), 0) AS amount
FROM transactions
WHERE purchase_date BETWEEN NOW() - INTERVAL 7 DAY AND NOW()
AND vendor_id = 0
GROUP BY purchase_date
)t2
on t2.purchase_date = t1.purchase_date
group by t1.purchase_date
order by t1.purchase_date desc
DEMO
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