Problems updating with inner join with multiple on statements
First, you have conditions duplicated in the ON and the WHERE clause. That is not needed, the condition are only needed once, preferably in the ON clause as they are used for the join of the two tables. But that is not what's causing the slow execution (and the lost connections).

The reasons for being slow are three:


you are joining a 63K with a 363K table without any index to help. That is the major issue.
the columns used in the join do not have same type, length, character set and collation. This is another major issue, worse than the first. Even if you add indexes, but keep the same types, the indexes will not be of much help. More seriously, it's a question if you can / are allowed to change the types or the applications depend on the existing types.
you are updating potentially the whole table. This is rather minor as the table is small, only 63K rows. We'll see if that is still a problem, after we fix the major issues.


The first thing that needs addressing is the types (+ lengths + charsets + collations) of the two columns. Assuming that you are allowed to change the types of the table order, you should change the types (both varchar(255) COLLATE utf8_unicode_ci DEFAULT NULL) to match the types of the geo table (one varchar(50), the other char(2), both CHARSET=latin1, unknown/default collation.)

This will be tricky and perhaps error prone, so I suggest you first take a backup of the whole database, or just the table orders, before you attempt to change anything.

If I were you, I'd then first (before changing anything), check the data in these two columns and whether their maximum length is less than 50 and 2 respectively, to be sure that the truncation of the length will not change any valuable data.

I'd also check the collation of the cities_extended.city and cities_extended.state_code columns, it's probably the default latin1_swedish_ci.

(Of course these two steps above can be skipped - but only if you don't really care about the orders table and you can recreate it from scratch if needed.)

After everything is double checked, we can proceed with the actual changing of the types:

ALTER TABLE ProcurementPortal.orders
    MODIFY COLUMN oCity 
        varchar(50) 
        CHARSET 'latin1'
        -- COLLATE 'latin1_swedish_ci'
        DEFAULT NULL,
    MODIFY COLUMN oState 
        char(2) 
        CHARSET 'latin1' 
        -- COLLATE 'latin1_swedish_ci'
        DEFAULT NULL ;


(the COLLATE 'latin1_swedish_ci' are probably not needed, the defaults will be used, so they are commented out.)

If that goes well and there are no errors, we can proceed with the final step, which is to add the indexes:

Add two indexes, one on each table:

ALTER TABLE ProcurementPortal.orders
   ADD INDEX state_city_ix
       (oState, oCity) ;

ALTER TABLE ProcurementPortal.cities_extended
   ADD INDEX state_city_ix
       (state_code, city) ;


After that (it will take a while but you only need to do this once), you can proceed with the update statement.

If it's still taking too long, I'd consider making the update in batches (of say 1K-5K rows per time). But with so small tables, I don't think you need that.