DECLARE @outlook nvarchar(max)='Something.something@email.com;Anne Hathaway < Anne.Hathaway@Email.com >; Albert Einstein < Albert.Einstein@email.com >; Ash Ketchum < Ash.Ketchum@mail.com >';

WITH semi AS (
    SELECT CAST(NULL AS nvarchar(255)) AS part, @outlook AS remain
    UNION ALL
    SELECT CAST(LEFT(remain, CHARINDEX(';', remain+';')-1) AS nvarchar(255)),
           CAST(SUBSTRING(remain, CHARINDEX(';', remain+';')+1, LEN(remain)) AS nvarchar(max))
    FROM semi
    WHERE remain!='')

SELECT +LEFT(addr, CHARINDEX('>', addr+'>')-1)
FROM (
    SELECT LTRIM(SUBSTRING(part, CHARINDEX('<', part)+1, LEN(part))) AS addr
    FROM semi
    WHERE part IS NOT NULL
    ) AS sub;

WITH semi AS (
    SELECT CAST(NULL AS nvarchar(255)) AS part, @outlook AS remain
    UNION ALL
    SELECT CAST(LEFT(remain, CHARINDEX(';', remain+';')-1) AS nvarchar(255)),
           CAST(SUBSTRING(remain, CHARINDEX(';', remain+';')+1, LEN(remain)) AS nvarchar(max))
    FROM semi
    WHERE remain!='')

SELECT SUBSTRING(CAST((
    SELECT '; '+LEFT(addr, CHARINDEX('>', addr+'>')-1)
    FROM (
        SELECT LTRIM(SUBSTRING(part, CHARINDEX('<', part)+1, LEN(part))) AS addr
        FROM semi
        WHERE part IS NOT NULL
        ) AS sub
    FOR XML PATH(''), TYPE) AS nvarchar(max)), 3, 10000);

SELECT STRING_AGG(RTRIM(LTRIM(REPLACE(REPLACE(b.[value], '<', ''), '>', ''))), '; ')
FROM STRING_SPLIT(@outlook, ';') AS a
CROSS APPLY STRING_SPLIT(a.[value], ' ') AS b
WHERE b.[value] LIKE '%@%';