Analyze and Optimize a SQL Query

WEX issues fleet fuel cards that companies give their drivers. An engineer is reviewing the query below, which totals each card's fuel spend for the last 30 days and reports the merchant category of its most recent purchase, for a fraud-monitoring dashboard. It's flagged as one of the slowest queries hitting the fuel_transactions table.

CREATE TABLE fleet_cards (
    card_id       BIGINT PRIMARY KEY,
    company_id     BIGINT,
    driver_name      TEXT
);

CREATE TABLE merchants (
    merchant_id   INT PRIMARY KEY,
    merchant_name  TEXT,
    category         TEXT     -- 'fuel', 'maintenance', 'toll', 'other'
);

CREATE TABLE fuel_transactions (
    transaction_id  BIGINT PRIMARY KEY,
    card_id          BIGINT REFERENCES fleet_cards(card_id),
    merchant_id       INT REFERENCES merchants(merchant_id),
    amount             NUMERIC(10,2),
    txn_time            TIMESTAMP
);
CREATE INDEX idx_fuel_txn_time ON fuel_transactions(txn_time);

SELECT
    fc.card_id,
    fc.driver_name,
    SUM(ft.amount) AS total_spend,
    (SELECT m.category FROM merchants m
       JOIN fuel_transactions ft2 ON ft2.merchant_id = m.merchant_id
       WHERE ft2.card_id = fc.card_id
       ORDER BY ft2.txn_time DESC LIMIT 1) AS last_category
FROM fleet_cards fc
JOIN fuel_transactions ft ON ft.card_id = fc.card_id
WHERE CAST(ft.txn_time AS DATE) >= CURRENT_DATE - 30
GROUP BY fc.card_id, fc.driver_name
HAVING SUM(ft.amount) > 500 OR COUNT(ft.transaction_id) > 40
ORDER BY total_spend DESC;

How would you analyze this given query and optimize it?