[RPG] What book had Rituals to “upgrade” animal companions to keep them viable at higher levels

No. From the SRD, Natural Weapons:

Creatures do not receive additional attacks from a high base attack bonus when using natural weapons.

The "Rules of the Game" column is describing the effects of a Druid class feature, which grants Multiattack to animal companions even if they don't have the prerequisites, and grants a bonus attack if they normally have only one attack. The extra attack has nothing to do with BAB and two attacks is all that Druid's wolf can have, regardless of the Druid's level.

The Ranger's entry for Animal Companions (page 48 of the Player's Handbook) specifically states

This ability functions like the druid ability of the same name, except that the ranger’s effective druid level is one-half his ranger level.

So Rangers also require 24 hours of uninterrupted time to replace a released or dead animal companion.

While there is nothing within the Player's Handbook regarding how the an animal companion is acquired, there is a section within Masters of the Wild that gives a more expansive set of rules on animal companions (page 34 onward). Please note though that Masters of the Wild is a 3e book, not 3.5, and as such certain elements of it have been superseded and other elements don't make a lot of sense (eg. the animal companion spell talked about in Masters of the Wild does not exist in 3.5), but it still does add a number of much more flavourful rules to a character's interaction with their companion.

As you surmise, the Animal Companion ability is not a magical effect - the animal does not simply "pop" into being like a summoned monster, the character must search within the typical terrain and climate that is home to the animal they are desiring. As such a dead animal companion would also leave a corpse like any other dead character within the party.

Masters of the Wild also requires a potentially greater amount of time to find an animal, saying that with a successful Wilderness Lore check to determine the animal's native terrain and climate and with the use of the detect animals or plants spell, that the character has a 30% chance per day of finding an animal of the desired type. While this is a much more flavourful rule for finding an animal companion, I can also understand why 3.5 has made this a flat 24 hour period without the need for spells or skills.

Masters of the Wild also expands on the bond between the PC and the animal, stating that it is a friend, not a slave, and it may grow tired of ill-treatment or constant damage-taking in fights. While the animal starts with an attitude of helpful, the GM should adjust the animal's attitude on the NPC Attitude table on page 149 of the Dungeon Master's Guide due to neglect or abuse, and that an animal that becomes hostile or unfriendly will do its best to leave the PC.

One further thing that your Ranger and Druid should consider is that Masters of the Wild classes abandoning a companion animal in a foreign land/terrain/climate, or the depths of a dungeon where most animals would not be comfortable, as an evil act, and that even neutral or evil Druids/Rangers would generally be against this practice.