By Leika Kihara TOKYO (Reuters) – Worries over a global slowdown are casting a shadow over Asia’s recovery prospects with factory activity growth slowing in Japan and Australia, keeping pressure on policymakers to support their economies while tightening monetary policy to combat inflation. Japan’s manufacturing activity grew at the slowest pace in 10 months in July, the purchasing managers’ index (PMI) survey showed on Friday, boding ill for an economy struggling to shake the wounds from the pandemic. Factory activity also slowed in Australia with the index falling to 55.7 in July from 56.2 i…