as @renjith.nair stated in the comments, I believe what you're after is simply
index="search_index" search processing_service | eval time_in_mins=('metric_value')/60 | stats avg(time_in_mins) as all_channel_avg
which would just output one column named all_channel_avg and one row with the avg.
if you'd like both the individual channel avg AND the total avg, possibly something like:
index="search_index" search processing_service | eval time_in_mins=('metric_value')/60 |eventstats avg(time_in_mins) as total_avg| stats values(total_avg) as all_channel_avg avg(time_in_mins) as channel_avg by channel
however, you might want to do a count and sum in the stats command and then the eventstats and some eval in order to not run eventstats before stats.
index="search_index" search processing_service | eval time_in_mins=('metric_value')/60| stats avg(time_in_mins) as channel_avg sum(time_in_mins) as total_mins count as total_count by channel|eventstats sum(total_mins) as total_mins sum(total_count) as total_count|eval all_channel_avg=total_mins/total_count
again, that might actually need some work, as i'm currently really thinking that the math might not be right....
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