Share balance is a column on every register, not only a register scoped to one security: the share balance of that row's own security after the row, computed over that security's complete ledger, using the same share-change rule and split adjustment the holdings and cost-basis engines use, and only then filtered, sorted, and shown. A sale of 20 after an earlier purchase of 100 still reads 80 even when the purchase falls outside the selected date range, because the figure is attached before the range narrows anything. Two securities traded on the same day never enter each other's figure.
A row on the account's cash ticker, or on a money-market vehicle it has swept into, leaves the cell empty: those shares are core cash, and the Cash balance column beside it states them. Scoping to one security shows the same figures on the same rows.
A small † marks an intermediate same-day balance: a later row of the same security recorded on the same date changes the figure again, so what you see is the balance in display order, not necessarily the day's last word on the position. Each security's last row equals the share count the account's own Positions tab reports for it.
The column shows only when the register is sorted by Date. Sorting by Activity, Security, Shares, Price or Amount blanks it, along with the Cash balance column, and one line above the table offers Sort by date to bring both back. A value's place in a re-sorted list would misstate a running total, so the register only declines to show it; it never recomputes it.