How did pastoral innovations in transportation (chariots, horses) and weaponry (bows, iron) transform warfare?

Technology changes such as you mentioned made war a lot more deadly and expensive. The more complicated the weapon the more energy and eventually money it cost to make it The more difficult to make the less were made So the following changes come

Capturing and raising horses costs money that most people could not afford so only rich people could do it. It is no coincidence that the word for knight in certain languages means rider - cavalier ritter etc Similarly armor also takes time and money to make so only rich people could afford it or if you did not have rich men you levied taxes to pay for it.

The more specialized the weapon for example a chariot or bow the more training and expertise is required to use it properly. Taking men away to train meant they were no longer available to work so replacements were needed. Professional warriors arose whose only job was to fight. Thy could do so all year round In former mass armies the army were the workers and had to go home to gather the harvest or sew new crops.A professional army supplied by others could stay in the field longer

If you had a large army another form of replacement labor were slaves as used in places lie Rome. Before a freeman could do al the work but when he had to fight a slave was useful

This also encouraged the rise f cities A lot of people living together provided both the labor to make te weapons and man the army A large group could also defend itself easier and build fortifications etc.